Question 301
The elements which are not capable of delivering energy on their own are known as:
Options:
- A) Unilateral elements
- B) Non-linear elements
- C) Passive elements
- D) Active elements
Answer: C) Passive elements
Step-by-Step Solution:
Passive elements cannot generate electrical energy by themselves. They can only:
- Absorb energy
- Store energy
- Dissipate energy
Examples of passive elements include resistors, inductors, and capacitors.
Therefore, elements that cannot deliver energy on their own are called passive elements.
Important Notes:
- Passive elements: Resistor (R), Inductor (L), Capacitor (C)
- Cannot generate electrical energy.
- Resistors dissipate energy.
- Inductors and capacitors store energy temporarily.
✔ Answer: C) Passive elements
Question 302
A network having one or more sources of EMF is known as:
Options:
- A) Passive network
- B) Active network
- C) Linear network
- D) Non-linear network
Answer: B) Active network
Step-by-Step Solution:
A network containing one or more energy sources, such as:
- Voltage source (EMF source)
- Current source
is called an active network because it can supply electrical energy to the load.
Important Notes:
-
Active network contains at least one:
- Voltage source
- Current source
- Can deliver power to a load.
- Examples: Battery circuits, Generator circuits.
✔ Answer: B) Active network
Question 303
A circuit having neither any energy source nor EMF source is called a:
Options:
- A) Unilateral circuit
- B) Bilateral circuit
- C) Passive circuit
- D) Active circuit
Answer: C) Passive circuit
Step-by-Step Solution:
A passive circuit contains only passive components such as:
- Resistors
- Inductors
- Capacitors
It does not contain any voltage source or current source.
Therefore, it cannot generate electrical energy.
Important Notes:
- Passive circuits contain only R, L and C elements.
- They cannot supply electrical energy.
- They only absorb, store or dissipate energy.
✔ Answer: C) Passive circuit
Question 304
A passive network has:
Options:
- A) No current source
- B) No EMF source
- C) Only EMF source
- D) Neither current source nor EMF source
Answer: D) Neither current source nor EMF source
Step-by-Step Solution:
A passive network consists only of passive components such as:
- Resistors
- Inductors
- Capacitors
It does not contain:
- Voltage (EMF) sources
- Current sources
Hence, a passive network has neither a current source nor an EMF source.
Important Notes:
- Passive Network = Only R, L and C elements.
- Active Network = Contains one or more voltage or current sources.
- Passive networks cannot generate electrical energy.
✔ Answer: D) Neither current source nor EMF source
Question 305
A terminal where more than two branches meet is known as:
Options:
- A) Node
- B) Terminus
- C) Anode
- D) None of these
Answer: A) Node
Step-by-Step Solution:
A node is a point in an electrical circuit where two or more circuit elements are connected.
When three or more branches meet at a common point, it is called an essential node.
Nodes are used in Nodal Analysis, where Kirchhoff's Current Law (KCL) is applied.
Important Notes:
- Node: Point where two or more circuit elements are connected.
- Essential Node: Point where three or more branches meet.
- KCL (Kirchhoff's Current Law) is applied at nodes.
- Nodal Analysis is used to determine node voltages.
✔ Answer: A) Node
Question 306
If a network has e elements and n nodes, the number of independent meshes is:
Options:
- A) n − 1
- B) e
- C) e − n
- D) (e − n) + 1
Answer: D) (e − n) + 1
Step-by-Step Solution:
For a connected electrical network, the number of independent meshes is given by:
Number of Independent Meshes = e − n + 1
where,
- e = Number of elements (or branches)
- n = Number of nodes
Therefore,
Number of Independent Meshes = (e − n) + 1
Hence, the correct answer is Option D.
Important Notes:
Basic Network Topology Formulas:
- Number of Independent Meshes = e − n + 1
- Number of Trees = n − 1
- Number of Links (Chords) = e − n + 1
These formulas are widely used in Mesh Analysis and Network Topology.
✔ Answer: D) (e − n) + 1
Question 308
For determining the polarity of the voltage drop across a resistor, we do not require the value of:
Options:
- A) Resistance
- B) Current
- C) EMF in the circuit
- D) All of these
Answer: D) All of these
Step-by-Step Solution:
The polarity of the voltage drop across a resistor is determined using the Passive Sign Convention.
According to this convention:
- The terminal where current enters is positive (+).
- The terminal where current leaves is negative (−).
To determine only the polarity, the numerical values of:
- Resistance
- Current
- Source EMF
are not required.
Only the direction of current flow is sufficient.
Therefore, the correct answer is Option D.
Important Notes:
-
Passive Sign Convention:
- Current enters the positive terminal.
- Current leaves the negative terminal.
- Voltage polarity depends on the direction of current, not on the magnitude of resistance or source voltage.
✔ Answer: D) All of these
Question 309
Kirchhoff's Laws are valid for:
Options:
- A) Linear circuits only
- B) Passive time-invariant circuits
- C) Non-linear circuits only
- D) Both linear and non-linear circuits
Answer: D) Both linear and non-linear circuits
Step-by-Step Solution:
Kirchhoff's Laws include:
- Kirchhoff's Current Law (KCL) – Based on the conservation of charge.
- Kirchhoff's Voltage Law (KVL) – Based on the conservation of energy.
These fundamental laws are applicable to both linear and non-linear circuits, provided the circuit can be analyzed using the lumped-parameter model.
Therefore, the correct answer is Option D.
Important Notes:
- KCL: Sum of currents entering a node equals the sum of currents leaving the node.
- KVL: Sum of voltages around any closed loop is zero.
-
Applicable to:
- Linear circuits
- Non-linear circuits
- AC circuits
- DC circuits
✔ Answer: D) Both linear and non-linear circuits
Question 310
Kirchhoff's Laws are applicable to circuits with:
Options:
- A) Lumped parameters
- B) Passive elements
- C) Non-linear resistances
- D) All of these
Answer: A) Lumped parameters
Step-by-Step Solution:
Kirchhoff's Laws assume that all circuit parameters such as resistance, inductance, and capacitance are concentrated at discrete locations. Such circuits are known as lumped parameter circuits.
In these circuits, the physical dimensions are much smaller than the wavelength of the electrical signal, allowing voltage and current to be considered uniform within each element.
Therefore, Kirchhoff's Laws are applicable to lumped parameter circuits.
Important Notes:
- Kirchhoff's Laws are applicable to lumped parameter circuits.
- They are generally not applicable to distributed parameter circuits, such as long transmission lines at high frequencies.
-
Lumped circuit elements include:
- Resistance (R)
- Inductance (L)
- Capacitance (C)
✔ Answer: A) Lumped parameters
Question 311
Kirchhoff's Voltage Law (KVL) is concerned with:
Options:
- A) IR drops
- B) Battery EMFs
- C) Both (A) and (B)
- D) None of the above
Answer: C) Both (A) and (B)
Step-by-Step Solution:
Kirchhoff's Voltage Law (KVL) states that:
The algebraic sum of all voltages around any closed loop is zero.
These voltages include:
- Voltage drops across resistors (IR drops)
- Voltage rises produced by batteries or voltage sources (EMFs)
Therefore, KVL considers both voltage drops and voltage rises.
Hence, the correct answer is Option C.
Important Notes:
- KVL is based on the Law of Conservation of Energy.
- Sum of Voltage Rises = Sum of Voltage Drops.
- KVL is applied in Mesh Analysis.
- Applicable to both AC and DC circuits.
✔ Answer: C) Both (A) and (B)
Question 312
Maxwell's Circulating Current Theorem:
Options:
- A) Utilizes Kirchhoff's Voltage Law
- B) Utilizes Kirchhoff's Current Law
- C) Is a network reduction method
- D) Is confined to single-loop circuits
Answer: A) Utilizes Kirchhoff's Voltage Law
Step-by-Step Solution:
Maxwell's Circulating Current Theorem is another name for the Mesh Current Method.
It determines the unknown mesh currents by applying Kirchhoff's Voltage Law (KVL) to each independent mesh of the circuit.
Therefore, it utilizes KVL.
Important Notes:
- Maxwell's Circulating Current Method = Mesh Analysis.
- Based on Kirchhoff's Voltage Law (KVL).
- Mainly applicable to planar networks.
- Used to determine unknown mesh currents.
✔ Answer: A) Utilizes Kirchhoff's Voltage Law
Question 313
The Superposition Theorem can be applied only to:
Options:
- A) Linear networks
- B) Non-linear networks
- C) Linear bilateral networks
- D) Bilateral networks
Answer: C) Linear bilateral networks
Step-by-Step Solution:
The Superposition Theorem is valid only when the circuit follows the principle of linearity.
The network should also be bilateral, meaning its characteristics remain the same regardless of the direction of current flow.
Therefore, the theorem is applicable only to linear bilateral networks.
Important Notes:
- Applicable only to linear bilateral networks.
- Only one independent source is considered at a time.
- Voltage sources are replaced by short circuits.
- Current sources are replaced by open circuits.
- Dependent sources remain active during analysis.
✔ Answer: C) Linear bilateral networks
Question 314
The Superposition Theorem is essentially based on the concept of:
Options:
- A) Reciprocity
- B) Linearity
- C) Duality
- D) Non-linearity
Answer: B) Linearity
Step-by-Step Solution:
The Superposition Theorem states that the total response in a linear circuit containing multiple independent sources is equal to the algebraic sum of the responses produced by each source acting individually.
This principle is valid only because the circuit satisfies the principle of linearity.
Therefore, the theorem is based on linearity.
Important Notes:
- Superposition depends on the Principle of Linearity.
-
Not applicable to non-linear devices such as:
- Diodes
- Transistors
- SCRs
- Used for calculating voltages and currents in linear circuits.
✔ Answer: B) Linearity
Question 315
The Superposition Theorem is applicable to:
Options:
- A) Current only
- B) Voltage only
- C) Power only
- D) All of these
Answer: D) All of these (As per the given answer key)
Step-by-Step Solution:
The Superposition Theorem is used to determine:
- Branch currents
- Branch voltages
Once the final voltage or current is obtained by superposition, the corresponding power can be calculated.
According to the given options and the provided answer key, the correct answer is Option D.
Important Notes:
-
Superposition is directly applied to:
- Voltage
- Current
- Power is not directly superimposed because power is a non-linear quantity.
-
First determine the resultant voltage or current, then calculate power using:
- P = VI
- P = I²R
- P = V²/R
Exam Tip:
Many competitive exams consider "All of these" as the expected answer. However, technically, the Superposition Theorem applies directly only to linear quantities (voltage and current). Power must always be calculated after obtaining the final voltage or current.
✔ Answer: D) All of these
Question 316
The Superposition Theorem requires as many circuit solutions as there are:
Options:
- A) Nodes
- B) Sources
- C) Nodes and Sources
- D) Meshes
Answer: B) Sources
Step-by-Step Solution:
According to the Superposition Theorem, only one independent source is kept active at a time, while all other independent sources are deactivated.
For example:
- If a circuit has 2 independent sources, solve 2 circuits.
- If a circuit has 5 independent sources, solve 5 circuits.
Thus, the number of circuit solutions required is equal to the number of independent sources.
Important Notes:
- Applicable only to linear bilateral networks.
- Independent voltage source → Replace with Short Circuit.
- Independent current source → Replace with Open Circuit.
- Dependent (controlled) sources are never turned off.
✔ Answer: B) Sources
Question 317
While obtaining the Thevenin equivalent between two terminals, the Thevenin voltage (VTH) is equal to:
Options:
- A) Short-circuit terminal voltage
- B) Open-circuit terminal voltage
- C) Net voltage available in the circuit
- D) None of these
Answer: B) Open-circuit terminal voltage
Step-by-Step Solution:
According to Thevenin's Theorem, the Thevenin voltage (VTH) is the voltage measured across the output terminals when no load is connected.
This condition is known as the open-circuit condition.
Therefore,
VTH = VOC
where:
- VTH = Thevenin Voltage
- VOC = Open-Circuit Voltage
Important Notes:
- VTH is always measured under open-circuit conditions.
- Remove the load resistor while calculating VTH.
-
Thevenin equivalent circuit consists of:
- VTH in series with RTH.
✔ Answer: B) Open-circuit terminal voltage
Question 318
Thevenin resistance (RTH) is determined:
Options:
- A) By short-circuiting the given two terminals
- B) By removing the voltage sources along with their internal resistances
- C) Between the same open terminals as for VTH
- D) None of these
Answer: C) Between the same open terminals as for VTH
Step-by-Step Solution:
After determining the Thevenin voltage (VTH), the Thevenin resistance (RTH) is calculated between the same two output terminals.
To determine RTH:
- Remove the load resistor.
-
Deactivate all independent sources:
- Voltage sources → Replace with Short Circuits.
- Current sources → Replace with Open Circuits.
- Find the equivalent resistance seen from the same output terminals.
Therefore, RTH is determined between the same open terminals used for VTH.
Important Notes:
- RTH is the equivalent resistance seen from the load terminals.
- Independent Voltage Source → Short Circuit.
- Independent Current Source → Open Circuit.
-
Thevenin equivalent circuit consists of:
- VTH in series with RTH.
✔ Answer: C) Between the same open terminals as for VTH
Question 319
In Thevenin's Theorem, the equivalent impedance (ZTH) is determined by:
Options:
- A) Short-circuiting all independent current and voltage sources
- B) Open-circuiting all independent current and voltage sources
- C) Short-circuiting all independent voltage sources and open-circuiting all independent current sources
- D) Open-circuiting all independent voltage sources and short-circuiting all independent current sources
Answer: C) Short-circuiting all independent voltage sources and open-circuiting all independent current sources
Step-by-Step Solution:
To determine the Thevenin impedance (ZTH):
- Remove the load.
-
Deactivate all independent sources:
- Independent voltage sources → Replace with Short Circuits.
- Independent current sources → Replace with Open Circuits.
- Calculate the equivalent impedance seen from the output terminals.
Hence, the correct answer is Option C.
Important Notes:
- Voltage Source OFF → Short Circuit.
- Current Source OFF → Open Circuit.
- Dependent (controlled) sources remain active.
-
For DC circuits:
ZTH = RTH
✔ Answer: C) Short-circuiting all independent voltage sources and open-circuiting all independent current sources
Question 320
The theorem applicable to both linear and non-linear circuits is:
Options:
- A) Superposition Theorem
- B) Thevenin's Theorem
- C) Norton's Theorem
- D) None of these
Answer: D) None of these
Step-by-Step Solution:
- Superposition Theorem is applicable only to linear circuits.
- Thevenin's Theorem is applicable only to linear bilateral circuits.
- Norton's Theorem is also applicable only to linear bilateral circuits.
Therefore, none of these theorems is applicable to both linear and non-linear circuits.
Important Notes:
- Superposition Theorem → Linear circuits only.
- Thevenin's Theorem → Linear bilateral circuits only.
- Norton's Theorem → Linear bilateral circuits only.
- Kirchhoff's Laws are valid for both linear and non-linear circuits.
✔ Answer: D) None of these
Question 321
While determining RTH in Thevenin's and Norton's equivalent circuits, which sources are made inactive?
Options:
- A) Only current sources
- B) Only voltage sources
- C) All independent sources
- D) All current and voltage sources
Answer: C) All independent sources
Step-by-Step Solution:
To calculate Thevenin Resistance (RTH) or Norton Resistance (RN):
- Replace all independent voltage sources with short circuits.
- Replace all independent current sources with open circuits.
- Dependent (controlled) sources remain active.
Therefore, all independent sources are made inactive.
Important Notes:
- Independent Voltage Source → Short Circuit.
- Independent Current Source → Open Circuit.
- Dependent (Controlled) Sources remain active.
- The same procedure is used for both Thevenin and Norton equivalent circuits.
✔ Answer: C) All independent sources
Question 322
For a linear network containing generators and impedances, the ratio of voltage to current remains the same even if the positions of the voltage source and the current-measuring instrument are interchanged. This theorem is known as:
Options:
- A) Millman's Theorem
- B) Norton's Theorem
- C) Tellegen's Theorem
- D) Reciprocity Theorem
Answer: D) Reciprocity Theorem
Step-by-Step Solution:
The Reciprocity Theorem states that in a linear bilateral network, if the positions of the excitation source and the response are interchanged, the ratio of excitation to response remains unchanged.
Therefore,
V₁ / I₂ = V₂ / I₁
Hence, the correct answer is Reciprocity Theorem.
Important Notes:
- Applicable only to linear bilateral networks.
- Not applicable to circuits containing dependent sources.
- The positions of the source and response can be interchanged without changing the transfer ratio.
✔ Answer: D) Reciprocity Theorem
Question 323
Nodal analysis is primarily based on the application of:
Options:
- A) Ohm's Law
- B) Kirchhoff's Current Law (KCL)
- C) Both (A) and (B)
- D) None of the above
Answer: C) Both (A) and (B)
Step-by-Step Solution:
In Nodal Analysis:
- Kirchhoff's Current Law (KCL) is applied at each node.
- Ohm's Law is used to express branch currents in terms of node voltages.
Thus, both laws are required to determine the node voltages.
Therefore, the correct answer is Option C.
Important Notes:
- Nodal Analysis is mainly used to determine node voltages.
- KCL is applied at every node.
- Ohm's Law is used to convert current equations into voltage equations.
- Widely used for solving complex electrical networks.
✔ Answer: C) Both (A) and (B)
Note: The source answer key lists Option D, but that is incorrect. The correct answer is Option C.
Question 324
In the node-voltage method of circuit analysis, the choice of the reference (ground) node:
Options:
- A) Affects the voltages of various nodes
- B) Affects the operation of the circuit
- C) Changes the voltage across any element
- D) Alters the potential difference between any pair of nodes
Answer: A) Affects the voltages of various nodes
Step-by-Step Solution:
In the node-voltage method, the reference (ground) node is assigned a voltage of 0 V.
Changing the reference node changes the numerical values of all node voltages because they are measured with respect to the selected reference.
However:
- The operation of the circuit remains unchanged.
- The voltage across any circuit element remains unchanged.
- The potential difference between any two nodes remains unchanged.
Therefore, only the node voltage values are affected.
Important Notes:
- The reference node is also called the Ground Node.
- Any node can be selected as the reference node.
- Choosing the node with the maximum number of connections simplifies calculations.
- Only the absolute node voltages change; the circuit behavior remains unchanged.
✔ Answer: A) Affects the voltages of various nodes
Question 325
When an uncharged body is placed near a charged body, the uncharged body:
Options:
- A) Is attracted first and then charged by induction.
- B) Gets charged by induction and then attracted towards the charged body.
- C) Gets charged by conduction.
- D) Remains unchanged.
Answer: B) Gets charged by induction and then attracted towards the charged body.
Step-by-Step Solution:
When a charged body is brought near an uncharged conductor:
- Charges inside the uncharged body redistribute due to the electric field.
- This process is called electrostatic induction.
- The side nearer to the charged body acquires an opposite charge, while the farther side acquires a like charge.
- As a result, the uncharged body experiences an attractive force and moves toward the charged body.
Therefore, the uncharged body first gets charged by induction and is then attracted toward the charged body.
Important Notes:
- Charging by induction occurs without direct contact.
- Opposite charges attract each other.
- Electrostatic induction takes place only when a charged body is brought near a conductor.
- No actual transfer of charge occurs between the two bodies.
✔ Answer: B) Gets charged by induction and then attracted towards the charged body.
Question 326
The value of electric field intensity due to a point charge can be determined by:
Options:
- A) Gauss's Law
- B) Ampere's Law
- C) Coulomb's Law
- D) Maxwell's Law
Answer: C) Coulomb's Law
Step-by-Step Solution:
The electric field intensity produced by a point charge is calculated using Coulomb's Law.
The electric field at a distance r from a point charge Q is given by:
E = (1 / 4πε) × (Q / r²)
where,
- E = Electric Field Intensity
- Q = Point Charge
- r = Distance from the charge
- ε = Permittivity of the medium
Therefore, the correct answer is Option C.
Important Notes:
- Electric field due to a point charge follows the Inverse Square Law.
- Electric field intensity is directly proportional to the magnitude of the charge.
- Electric field intensity is inversely proportional to the square of the distance.
-
SI Unit of Electric Field Intensity:
- N/C
- V/m
- Gauss's Law is generally used for symmetrical charge distributions.
✔ Answer: C) Coulomb's Law
Question 327
The space surrounding a charge within which its influence extends is known as:
Options:
- A) Electric field
- B) Magnetic field
- C) Lines of force
- D) Electric intensity
Answer: A) Electric field
Step-by-Step Solution:
A charged body creates an invisible region around itself where it exerts an electric force on other charged bodies.
This region is called the electric field.
Any charged particle entering this region experiences an electrostatic force.
Therefore, the correct answer is Option A.
Important Notes:
- An electric field exists around every electric charge.
- Electric field lines originate from positive charges and terminate on negative charges.
- Electric field intensity is represented by E.
-
SI Unit of Electric Field Intensity:
- V/m
- N/C
✔ Answer: A) Electric field
Question 328
The electric field intensity between the plates of a parallel-plate capacitor is E. If a dielectric of dielectric constant K is introduced between the plates (with the capacitor isolated), the electric field intensity becomes:
Options:
- A) KE
- B) E/K
- C) E
- D) K²E
Answer: B) E/K
Step-by-Step Solution:
When a dielectric having dielectric constant K is inserted into an isolated charged capacitor, the dielectric becomes polarized.
This polarization reduces the electric field inside the capacitor.
The new electric field intensity is:
E' = E / K
where,
- E = Original electric field intensity
- K = Dielectric constant (Relative Permittivity)
Therefore, the electric field decreases by a factor of K.
Important Notes:
-
Dielectric Constant:
K = εr
-
Inserting a dielectric into an isolated capacitor:
- Decreases electric field intensity.
- Increases capacitance.
-
Relation:
E' = E / K
✔ Answer: B) E/K
Question 329
For a perfect conductor:
Options:
- A) Dn = ρs
- B) Dn = 0
- C) Dn = ∞
- D) None of these
Answer: A) Dn = ρs
Step-by-Step Solution:
For a perfect conductor in electrostatic equilibrium:
- The electric field inside the conductor is zero.
- Any excess charge resides only on the outer surface.
According to the boundary condition,
Dn = ρs
where,
- Dn = Normal component of Electric Flux Density
- ρs = Surface Charge Density
Therefore,
Dn = ρs
Important Notes:
-
For a perfect conductor:
- E = 0 inside the conductor.
- Excess charge exists only on the outer surface.
-
Boundary condition:
Dn = ρs
- Electric field lines are always perpendicular to the conductor surface.
✔ Answer: A) Dn = ρs
Question 330
The equation ∮ D · dS = Q is based on:
Options:
- A) Ampere's Law
- B) Gauss's Law
- C) Faraday's Law
- D) Coulomb's Law
Answer: B) Gauss's Law
Step-by-Step Solution:
Gauss's Law states that the total electric flux passing through any closed surface is equal to the total charge enclosed by that surface.
Mathematically,
∮ D · dS = Q
where,
- D = Electric Flux Density
- dS = Differential Surface Area
- Q = Total Charge Enclosed
Hence, the given equation represents Gauss's Law.
Important Notes:
-
Integral form of Gauss's Law:
∮ D · dS = Q
-
Used to calculate electric fields for:
- Spherical symmetry
- Cylindrical symmetry
- Planar symmetry
- Based on the Law of Conservation of Electric Charge.
✔ Answer: B) Gauss's Law
Question 331
"The total electric flux through any closed surface surrounding charges is equal to the amount of charge enclosed." This statement is based on:
Options:
- A) Maxwell's Law
- B) Ampere's Law
- C) Gauss's Law
- D) Coulomb's Law
Answer: C) Gauss's Law
Step-by-Step Solution:
Gauss's Law states that the total electric flux passing through a closed surface is equal to the total charge enclosed within that surface.
Mathematically,
∮ E · dA = Qenclosed / ε₀
or
∮ D · dS = Q
where,
- E = Electric Field Intensity
- D = Electric Flux Density
- Q = Charge enclosed by the closed surface
- ε₀ = Permittivity of free space
Therefore, the given statement is based on Gauss's Law.
Important Notes:
- Gauss's Law relates electric flux to the enclosed electric charge.
- It is one of Maxwell's four equations.
-
Used to calculate electric fields with:
- Spherical symmetry
- Cylindrical symmetry
- Planar symmetry
✔ Answer: C) Gauss's Law
Question 332
Which of the following is a scalar quantity?
Options:
- A) Electric Field Strength
- B) Electric Flux Density
- C) Electric Potential
- D) Force
Answer: C) Electric Potential
Step-by-Step Solution:
A scalar quantity has only magnitude and no direction.
Among the given quantities:
- Electric Field Strength → Vector
- Electric Flux Density → Vector
- Electric Potential → Scalar
- Force → Vector
Therefore, Electric Potential is the only scalar quantity.
Important Notes:
Scalar Quantities:
- Electric Potential
- Charge
- Energy
- Work
Vector Quantities:
- Electric Field Intensity
- Electric Flux Density
- Force
- Magnetic Field Intensity
- SI Unit of Electric Potential = Volt (V)
✔ Answer: C) Electric Potential
Question 333
The electric potential due to an electric dipole of length l at a point located at a distance r is doubled if:
Options:
- A) The dipole length l is doubled.
- B) r is doubled.
- C) r is halved.
- D) l is halved.
Answer: A) The dipole length l is doubled.
Step-by-Step Solution:
The electric potential due to an electric dipole is directly proportional to its dipole moment.
Dipole Moment:
p = q × l
Since,
V ∝ p
and
p ∝ l
Therefore,
V ∝ l
If the dipole length is doubled,
l' = 2l
then,
V' = 2V
Hence, the electric potential also becomes twice its original value.
Important Notes:
-
Dipole Moment:
p = q × l
- Electric potential is directly proportional to the dipole moment.
- Increasing dipole length increases the electric potential.
- Electric potential decreases as the distance from the dipole increases.
✔ Answer: A) The dipole length l is doubled.
Question 334
The dielectric strength of a medium:
Options:
- A) Increases with an increase in temperature.
- B) Decreases with an increase in thickness.
- C) Increases with moisture content.
- D) Is not affected by moisture content.
Answer: B) Decreases with an increase in thickness
Step-by-Step Solution:
Dielectric strength is the maximum electric field that an insulating material can withstand without electrical breakdown.
In practice,
- As the thickness of the insulating material increases, its dielectric strength (expressed in kV/mm) decreases slightly due to the higher probability of internal defects and non-uniform electric fields.
Therefore, the dielectric strength decreases with increasing thickness.
Important Notes:
-
Dielectric Strength is measured in:
- kV/mm
- MV/m
- Moisture reduces the insulating capability of a dielectric.
- Higher temperature generally reduces dielectric strength.
- Good insulating materials have high dielectric strength.
✔ Answer: B) Decreases with an increase in thickness
Question 335
The time constant of an RC series circuit connected to a DC source is equal to:
Options:
- A) L/R
- B) R/C
- C) RC
- D) C/R
Answer: C) RC
Step-by-Step Solution:
The time constant of an RC circuit is the time required for the capacitor voltage to:
- Reach 63.2% of its final value during charging, or
- Fall to 36.8% of its initial value during discharging.
The time constant is given by:
τ = R × C
where,
- R = Resistance (Ω)
- C = Capacitance (F)
Therefore,
τ = RC
Important Notes:
-
RC Time Constant:
τ = RC
-
RL Time Constant:
τ = L / R
-
At one time constant (τ):
- Charging = 63.2%
- Discharging = 36.8%
- Unit of Time Constant = Second (s)
✔ Answer: C) RC
Question 336
The magnetic susceptibility of a paramagnetic material is:
Options:
- A) Less than zero
- B) Less than one but positive
- C) Greater than one
- D) Equal to zero
Answer: B) Less than one but positive
Step-by-Step Solution:
Magnetic susceptibility (χm) indicates how easily a material becomes magnetized when placed in an external magnetic field.
For paramagnetic materials:
- Magnetic susceptibility is positive.
- Its value is very small (less than one).
Therefore, paramagnetic materials are weakly attracted by a magnetic field.
Important Notes:
- Diamagnetic materials: χm < 0
- Paramagnetic materials: 0 < χm < 1
- Ferromagnetic materials: χm >> 1
-
Examples of paramagnetic materials:
- Aluminium
- Platinum
- Manganese
✔ Answer: B) Less than one but positive
Question 337
A keeper is used for:
Options:
- A) Restoring lost flux
- B) Amplification of flux
- C) Providing a closed path for the magnetic flux
- D) Changing the direction of magnetic lines of force
Answer: C) Providing a closed path for the magnetic flux
Step-by-Step Solution:
A keeper is a strip of soft iron placed across the poles of a permanent magnet.
It provides a closed magnetic path, which reduces magnetic reluctance and prevents loss of magnetism during storage.
Therefore, the main purpose of a keeper is to provide a closed path for magnetic flux.
Important Notes:
- A keeper is made of soft iron.
- It reduces magnetic leakage.
- It helps preserve the strength of permanent magnets during storage.
- Commonly used with horseshoe magnets.
✔ Answer: C) Providing a closed path for the magnetic flux
Question 338
The force experienced by a unit north pole at any point is known as:
Options:
- A) Magnetomotive Force (MMF)
- B) Magnetic Field Strength
- C) Magnetic Flux Density
- D) Magnetic Potential
Answer: B) Magnetic Field Strength
Step-by-Step Solution:
Magnetic Field Strength (H) is defined as the force experienced by a unit north pole placed at a point in a magnetic field.
It represents the intensity of the magnetic field at that location.
Therefore, the correct answer is Magnetic Field Strength.
Important Notes:
- Symbol: H
- SI Unit: A/m (Ampere per metre)
-
Relation:
B = μH
where:
- B = Magnetic Flux Density
- μ = Permeability of the medium
- H = Magnetic Field Strength
✔ Answer: B) Magnetic Field Strength
Question 339
Magnetic lines of force:
Options:
- A) Never intersect
- B) Often intersect
- C) Intersect only in special circumstances
- D) Are unpredictable
Answer: A) Never intersect
Step-by-Step Solution:
Magnetic field lines indicate the direction of the magnetic field.
If two magnetic field lines intersected, there would be two different directions of the magnetic field at the same point, which is impossible.
Therefore, magnetic lines of force never intersect.
Important Notes:
Properties of Magnetic Field Lines:
- They form closed loops.
- They never intersect each other.
- Outside a magnet, they flow from North Pole to South Pole.
- Inside a magnet, they flow from South Pole to North Pole.
✔ Answer: A) Never intersect
Question 340
Magnetostriction is the phenomenon in which the magnetization of a ferromagnetic material causes a change in its:
Options:
- A) Relative Permeability
- B) Physical Dimensions
- C) Spontaneous Magnetization
- D) Electrical Resistance
Answer: B) Physical Dimensions
Step-by-Step Solution:
Magnetostriction is the property of ferromagnetic materials in which their length or dimensions change slightly when they are magnetized.
Although the dimensional change is very small, it is sufficient to produce vibrations and the familiar humming sound in transformers.
Therefore, magnetization causes a change in the physical dimensions of the material.
Important Notes:
- Magnetostriction occurs only in ferromagnetic materials.
- It is responsible for the humming noise in transformers.
- The change in dimensions is very small and reversible under normal operating conditions.
-
Common ferromagnetic materials include:
- Iron
- Nickel
- Cobalt
✔ Answer: B) Physical Dimensions
Question 341
The equation ∮ B · dS = 0 is based on:
Options:
- A) Gauss's Law
- B) Ampere's Law
- C) Faraday's Law
- D) Ohm's Law
Answer: A) Gauss's Law
Step-by-Step Solution:
Gauss's Law for Magnetism states that the total magnetic flux passing through any closed surface is zero.
Mathematically,
∮ B · dS = 0
This means that magnetic field lines always form closed loops, and magnetic monopoles do not exist.
Therefore, the given equation is based on Gauss's Law for Magnetism.
Important Notes:
-
Gauss's Law for Magnetism:
∮ B · dS = 0
- Magnetic monopoles do not exist.
- Magnetic field lines always form closed loops.
- It is one of Maxwell's Equations.
✔ Answer: A) Gauss's Law
Question 342
The Biot-Savart Law is a general modification of:
Options:
- A) Coulomb's Law
- B) Ampere's Law
- C) Faraday's Law
- D) Ohm's Law
Answer: B) Ampere's Law
Step-by-Step Solution:
The Biot-Savart Law is used to calculate the magnetic field produced by a small current element.
It is a more general expression from which Ampere's Circuital Law can be derived for symmetrical current distributions.
Therefore, it is regarded as a general modification of Ampere's Law.
Important Notes:
- Biot-Savart Law calculates the magnetic field due to a current element.
-
Used for determining the magnetic field around:
- Straight conductors
- Circular loops
- Current elements
- SI Unit of Magnetic Flux Density = Tesla (T)
✔ Answer: B) Ampere's Law
Question 343
The direction of the mechanical force experienced by a current-carrying conductor placed in a magnetic field is determined by:
Options:
- A) Fleming's Left-Hand Rule
- B) Fleming's Right-Hand Rule
- C) Helix Rule
- D) Corkscrew Rule
Answer: A) Fleming's Left-Hand Rule
Step-by-Step Solution:
When a current-carrying conductor is placed in a magnetic field, it experiences a mechanical force.
The direction of this force is determined using Fleming's Left-Hand Rule.
According to the rule:
- Forefinger → Magnetic Field (B)
- Middle Finger → Current (I)
- Thumb → Force or Motion (F)
Therefore, the correct answer is Fleming's Left-Hand Rule.
Important Notes:
- Fleming's Left-Hand Rule is used for Motors.
- Fleming's Right-Hand Rule is used for Generators.
-
Force on a conductor:
F = B × I × L × sin θ
✔ Answer: A) Fleming's Left-Hand Rule
Question 344
If a current-carrying conductor is placed in a magnetic field, the mechanical force acting on the conductor is determined by:
Options:
- A) Simple product
- B) Dot product
- C) Cross product
- D) Any of these
Answer: C) Cross Product
Step-by-Step Solution:
The magnetic force acting on a current-carrying conductor is given by:
F = I (L × B)
Since the force is obtained by taking the cross product of the conductor length vector and the magnetic flux density vector, its magnitude is:
F = B × I × L × sin θ
Therefore, the force is determined by the cross product.
Important Notes:
-
Force Equation:
F = I (L × B)
-
Magnitude:
F = B × I × L × sin θ
-
Maximum force occurs when:
θ = 90°
-
Zero force occurs when:
θ = 0°
✔ Answer: C) Cross Product
Question 345
The force experienced by a current-carrying conductor lying parallel to a magnetic field is:
Options:
- A) Zero
- B) BIL
- C) BIL sin θ
- D) BIL cos θ
Answer: A) Zero
Step-by-Step Solution:
The force acting on a current-carrying conductor is given by:
F = B × I × L × sin θ
When the conductor is parallel to the magnetic field,
θ = 0°
Since,
sin 0° = 0
Therefore,
F = 0
Hence, no mechanical force acts on the conductor.
Important Notes:
-
Force Formula:
F = B × I × L × sin θ
- Maximum force occurs when the conductor is perpendicular to the magnetic field (θ = 90°).
- Zero force occurs when the conductor is parallel to the magnetic field (θ = 0°).
✔ Answer: A) Zero
Question 346
A straight conductor of length l moves with velocity v in a magnetic field of flux density B, making an angle θ with the direction of motion. Which of the following statements is correct?
- It is independent of θ.
- It is proportional to l².
- It is proportional to B.
- It is independent of v.
Options:
- A) 1, 2 and 3
- B) 4 alone
- C) 3 alone
- D) 2 and 4
Answer: C) 3 alone
Step-by-Step Solution:
The induced EMF in a moving conductor is given by:
e = B × l × v × sin θ
Similarly, the magnetic force on a current-carrying conductor is:
F = B × I × l × sin θ
From these equations:
- It is directly proportional to B. ✔
- It depends on θ, so Statement 1 is false.
- It is proportional to l, not l², so Statement 2 is false.
- It depends on v, so Statement 4 is false.
Therefore, only Statement 3 is correct.
Important Notes:
-
Induced EMF:
e = B × l × v × sin θ
-
Force on a conductor:
F = B × I × l × sin θ
-
Maximum value occurs when:
θ = 90°
-
Zero value occurs when:
θ = 0°
✔ Answer: C) 3 alone
Question 347
The magnetic field intensity (in A/m) at the center of a circular coil of diameter 1 m carrying a current of 2 A is:
Options:
- A) 8 A/m
- B) 4 A/m
- C) 3 A/m
- D) 2 A/m
Answer: D) 2 A/m
Step-by-Step Solution:
The magnetic field intensity at the center of a single-turn circular coil is:
H = I / (2R)
where,
- I = 2 A
- Diameter = 1 m
- Radius R = 0.5 m
Substituting the values:
H = 2 / (2 × 0.5)
H = 2 / 1
H = 2 A/m
Therefore, the magnetic field intensity is 2 A/m.
Important Notes:
-
Magnetic field intensity at the center of a circular coil:
H = I / (2R)
-
Magnetic flux density:
B = μH
- SI unit of Magnetic Field Intensity = A/m
✔ Answer: D) 2 A/m
Question 348
The magnetic field at any point on the axis of a current-carrying circular coil is:
Options:
- A) Perpendicular to the axis
- B) Parallel to the axis
- C) At an angle of 45°
- D) Zero
Answer: B) Parallel to the axis
Step-by-Step Solution:
The magnetic field produced by a current-carrying circular coil is directed along its axis.
At every point on the axis of the coil, the magnetic field remains parallel to the axis.
Therefore, the correct answer is Option B.
Important Notes:
- The magnetic field at the center of a circular coil is along its axis.
- Direction is determined using the Right-Hand Thumb Rule.
- The magnetic field is strongest at the center of the coil.
✔ Answer: B) Parallel to the axis
Question 349
Consider the following statements regarding the force between two parallel current-carrying conductors:
- The force per unit length is inversely proportional to the distance between the conductors.
- The force per unit length is directly proportional to the magnitude of each current.
- The force satisfies Newton's Third Law.
Options:
- A) 1 and 2 are correct
- B) 2 and 3 are correct
- C) 1 and 3 are correct
- D) 1, 2 and 3 are correct
Answer: D) 1, 2 and 3 are correct
Step-by-Step Solution:
The force per unit length between two long parallel current-carrying conductors is given by:
F/L = (μ₀ × I₁ × I₂) / (2π × d)
where,
- I₁ = Current in the first conductor
- I₂ = Current in the second conductor
- d = Distance between the conductors
From the formula:
- Force is directly proportional to I₁ and I₂. ✔
- Force is inversely proportional to the distance d. ✔
- The forces on the two conductors are equal and opposite, satisfying Newton's Third Law. ✔
Therefore, all three statements are correct.
Important Notes:
-
Force per unit length:
F/L = (μ₀ × I₁ × I₂) / (2π × d)
- Parallel currents in the same direction attract each other.
- Parallel currents in opposite directions repel each other.
- SI unit of Force per Unit Length = N/m.
✔ Answer: D) 1, 2 and 3 are correct
Question 350
Permeability is the reciprocal of:
Options:
- A) Reluctivity
- B) Susceptibility
- C) Permittivity
- D) Conductivity
Answer: A) Reluctivity
Step-by-Step Solution:
Permeability (μ) is the property of a material that indicates how easily it allows magnetic flux to pass through it.
Reluctivity (ν) is the reciprocal of permeability.
The relationship is:
ν = 1 / μ
or
μ = 1 / ν
Therefore, permeability is the reciprocal of reluctivity.
Important Notes:
-
Permeability:
μ = μ₀ × μr
where:
- μ₀ = Permeability of Free Space
- μr = Relative Permeability
-
Relation between Permeability and Reluctivity:
μ = 1 / Reluctivity
- SI Unit of Permeability = Henry per metre (H/m)
- Materials with high permeability allow magnetic flux to pass more easily.
✔ Answer: A) Reluctivity