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A dielectric is an insulating material that becomes polarized when it is placed in an electric field. In a capacitor, the dielectric separates the conducting plates and allows electrostatic energy to be stored while preventing significant direct current from flowing through the insulation. A good dielectric should therefore have very high insulation resistance, low leakage current, adequate dielectric strength and suitable permittivity. Common dielectric materials include mica, glass, ceramic, paper and suitable plastics.
For a parallel-plate capacitor, C = ÎľA/d. Here Îľ = Îľ₀ξᾣ is the permittivity of the dielectric. A higher ξᾣ allows greater capacitance for the same geometry.
đ Remember Points
đ Good dielectric → high insulation resistance
đ Dielectric strength → ability to withstand electric stress without breakdown
đ Dielectric stores energy through its electric field
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An electrolytic capacitor is generally a polarized capacitor, meaning its terminals have defined positive and negative polarity. It is primarily used in DC circuits such as rectifier filters, smoothing circuits and DC-link applications. The polarity must be observed. Reverse voltage or unsuitable AC operation can cause excessive leakage current, heating, gas generation and failure. Therefore, for the conventional objective-question answer, electrolytic capacitors are used for DC applications.
For a capacitor, i = C(dv/dt). A capacitor can carry AC current because its voltage changes continuously, but a polarized electrolytic capacitor is not normally connected directly to an arbitrary AC source.
đ Remember Points
đ Electrolytic → normally polarized
đ Commonly used for DC filtering/smoothing
đ Reverse polarity can damage the capacitor
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For an ideal parallel-plate capacitor, capacitance is determined by the effective plate area, separation between the plates and the permittivity of the material between them. The thickness of the metal plates does not directly appear in the capacitance equation, provided the active plate surfaces and their separation remain unchanged. Therefore, conductor thickness is the correct choice.
C = ÎľA/d. Thus C ∝ A, C ∝ 1/d, and C ∝ Îľ. Conductor thickness does not appear directly in this ideal expression.
đ Remember Points
đ Area ↑ → C ↑
đ Plate spacing ↑ → C ↓
đ Permittivity ↑ → C ↑
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A vector quantity has both magnitude and direction, whereas a scalar quantity has magnitude only. Linear momentum, angular momentum and electric field are vectors. Electric potential is a scalar because a potential value at a point does not have a direction. Therefore, electric potential is not a vector quantity.
Electric field: E⃗ = F⃗/Q, so it has direction. Electric potential V is scalar and has no direction.
đ Remember Points
đ Momentum → vector
đ Electric field → vector
đ Potential, energy and power → scalars
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After the capacitor is disconnected from the source, there is no conducting path for charge to leave the isolated plates, so the charge Q remains approximately constant. When the plates are separated, the plate spacing d increases. Since C = ÎľA/d, capacitance decreases. From V = Q/C, with Q constant, a decrease in C causes the voltage to increase. Hence the voltage rises.
C = ÎľA/d. If d ↑, then C ↓. For an isolated capacitor Q = constant, so V = Q/C and therefore V ↑ when C ↓.
đ Remember Points
đ Isolated capacitor → Q constant
đ Plate separation ↑ → C ↓
đ With Q constant → V ↑
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A capacitor does not allow continuous steady-state current for ideal DC, but it does conduct current whenever its voltage changes. An AC voltage continuously changes with time, so the capacitor is repeatedly charging and discharging. The resulting current is proportional to the rate of change of voltage. Thus, the changing voltage produces the alternating current.
i = dq/dt. Since q = Cv, i = C(dv/dt). For sinusoidal AC, capacitive reactance is Xc = 1/(2ĎfC).
đ Remember Points
đ i = C(dv/dt)
đ DC steady state → ideal capacitor current is zero
đ Higher frequency → lower Xc
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The source wording is physically inconsistent if it is interpreted literally for the same electric flux density. In a dielectric, D = ÎľE and Îľ = KÎľ₀, so E = D/(KÎľ₀). Therefore, for the same D, increasing K actually reduces E rather than making it 100 times larger. The intended textbook answer associates the factor 100 with the dielectric constant, so the expected answer is 100. This distinction is important for a technically correct understanding.
D = ÎľE = KÎľ₀E, hence E = D/(KÎľ₀). For the same D, E is inversely proportional to K.
đ Remember Points
đ Îľ = KÎľ₀
đ D = ÎľE
đ For fixed D → E ∝ 1/K
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Electrolytic capacitors are generally polarized. Their positive and negative terminals are marked, and the capacitor must be connected according to that polarity. Reverse connection can produce high leakage current, heating and potentially rupture. Ceramic and mica capacitors are generally non-polarized, so they do not normally require a fixed DC polarity.
A polarized capacitor requires correct terminal polarity. For an electrolytic capacitor, reverse voltage can produce excessive leakage and internal heating.
đ Remember Points
đ Electrolytic → polarized
đ Ceramic → generally non-polarized
đ Mica → generally non-polarized
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Dissipation factor, commonly represented by tan δ, indicates dielectric loss in an insulating material. A good dielectric has very small dielectric losses, so its dissipation factor is a small number. Among the given choices, 0.0002 represents the intended order. A lower loss tangent generally means lower dielectric heating and better dielectric performance.
Dissipation factor = tan δ. For a low-loss dielectric, tan δ is very small. Lower tan δ → lower dielectric loss.
đ Remember Points
đ tan δ represents dielectric loss
đ Lower tan δ → lower loss
đ Dielectric loss can cause heating
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Gauss's law relates the total electric flux through a closed surface to the net charge enclosed by that surface. It is especially useful for symmetrical charge distributions because the electric field can often be taken as constant over a Gaussian surface. The statement in the question is the integral form of Gauss's law.
∮ E⃗·dA⃗ = Qenc/Îľ. In terms of electric flux density, ∮ D⃗·dA⃗ = Qenc.
đ Remember Points
đ Gauss → electric flux and enclosed charge
đ Closed surface is essential
đ D-flux form: ∮D⃗·dA⃗ = Qenc
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First connect two identical capacitors in parallel. Their equivalent capacitance becomes 2C. Now connect this 2C combination in series with the remaining C capacitor. The series equivalent is the product divided by the sum, giving (2C × C)/(2C + C) = 2C/3. Therefore, option C is correct.
Parallel: Cp = C + C = 2C. Series: Ceq = (2C·C)/(2C + C) = 2C/3.
đ Remember Points
đ Parallel capacitors add directly
đ Series capacitors use reciprocal/product-over-sum relation
đ For two equal capacitors in series → C/2
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The ideal capacitance of a parallel-plate capacitor depends on plate area, plate separation and dielectric permittivity. The thickness of the conducting plates is not present in the basic capacitance equation. Therefore, if the separation between the active surfaces remains unchanged, increasing conductor thickness does not directly change capacitance.
C = ÎľA/d. Variables affecting C: Îľ, A and d. Conductor thickness is not a direct variable in the ideal equation.
đ Remember Points
đ A ↑ → C ↑
đ d ↑ → C ↓
đ Îľ ↑ → C ↑
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When a charged capacitor discharges through a resistor, its voltage and charge do not fall at a constant rate. Instead, they decrease exponentially. The current also follows an exponential decay. At the instant discharge begins, the current is maximum; as time becomes very large, the current approaches zero.
q(t) = Q₀e^(−t/RC), and i(t) = I₀e^(−t/RC). The time constant is Ď = RC.
đ Remember Points
đ Discharge current → exponential decay
đ Ď = RC
đ At t → ∞, current → 0
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Electric flux density D and electric field intensity E are related through the permittivity of the medium. The fundamental constitutive relation is D = ÎľE. Rearranging it gives E = D/Îľ. Therefore, option A is correct. The units are also consistent: D is C/m² and Îľ is F/m, giving E in V/m or N/C.
D = ÎľE, therefore E = D/Îľ. Here E is in V/m (or N/C), D in C/m² and Îľ in F/m.
đ Remember Points
đ D → electric flux density
đ E → electric field intensity
đ Îľ → permittivity
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The capacitor's conductors carry equal and opposite charges, but the energy is associated with the electric field established between the conductors. In a dielectric-filled capacitor, the field exists in the dielectric region. This distinction is important: charge is associated with the plates, while stored electromagnetic energy is represented by the electric field.
Total energy: W = ½CV². Energy density in a linear dielectric: u = ½ÎľE².
đ Remember Points
đ W = ½CV²
đ u = ½ÎľE²
đ Energy density describes energy per unit volume
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Relative permittivity or dielectric constant tells us how strongly a material increases capacitance compared with vacuum. Vacuum has K = 1, oil is relatively low, and glass is moderate. Many ceramic dielectric formulations can have very high dielectric constants, so ceramic is the best answer among the listed choices. The exact value depends on the ceramic composition.
K = Îľ/Îľ₀. For the same capacitor geometry, C = KÎľ₀A/d, so higher K gives higher capacitance.
đ Remember Points
đ Vacuum → K = 1
đ K has no unit
đ Higher K → higher C for the same geometry
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Mica is a highly stable dielectric with low dielectric loss and excellent temperature stability. Silver-plated mica capacitors are therefore traditionally used where capacitance must remain stable over temperature changes, particularly in precision and high-frequency circuits. The exact temperature coefficient depends on the particular capacitor construction.
Temperature coefficient of capacitance can be expressed approximately as ÎąC = (1/C)(dC/dT), often specified in ppm/°C.
đ Remember Points
đ Mica → stable capacitance
đ Low temperature coefficient → better stability
đ Useful in precision/high-frequency circuits
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The word “always” makes statement B incorrect. At constant voltage, capacitor energy is W = ½CV², so reducing C reduces energy. However, for an isolated capacitor where charge remains constant, W = Q²/(2C), so reducing C actually increases energy. Therefore, whether energy increases or decreases depends on which quantity is held constant.
At constant V: W = ½CV². At constant Q: W = Q²/(2C). Always identify the constraint before deciding how W changes.
đ Remember Points
đ Constant V → W ∝ C
đ Constant Q → W ∝ 1/C
đ The word “always” requires careful checking
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Electrolytic capacitors use an electrolyte system and are generally more sensitive to ageing and storage conditions than highly stable dielectric types such as mica and many ceramic capacitors. Long storage can affect electrolyte condition and leakage characteristics. Therefore, the conventional answer is electrolytic capacitor.
Capacitor reliability depends on temperature, leakage, electrolyte condition, dielectric ageing and storage history rather than a single universal formula.
đ Remember Points
đ Electrolytic → polarized
đ Electrolyte ageing can increase leakage
đ Mica/ceramic → generally strong long-term stability
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When current through an inductive load is interrupted, the magnetic energy stored in the inductance tries to keep the current flowing. This can produce a large transient voltage across the opening contacts and cause an arc. A capacitor connected across the contacts provides a path for the transient current and reduces the rate of voltage rise. An RC snubber is a common practical implementation.
Inductive transient voltage: v = L(di/dt). A suppression capacitor reduces the severity of the voltage transient across the switching contacts.
đ Remember Points
đ Inductor opposes sudden current change
đ v = L(di/dt)
đ RC snubber → switching transient suppression
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An ideal capacitor has no internal resistive loss, so its ideal ESR is zero. A real capacitor contains electrode resistance, internal connections, dielectric losses and, in electrolytic types, electrolyte resistance. These effects can be represented by an equivalent series resistance. For a good practical capacitor, ESR is usually small but not exactly zero.
Ideal capacitor: ESR = 0. Real capacitor: ESR > 0. Approximate resistive power loss is P_loss ≈ I_rms² × ESR.
đ Remember Points
đ Ideal ESR = 0
đ Real ESR > 0
đ Higher ESR generally means higher internal loss and heating
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In a pure capacitive AC circuit, current leads voltage by 90°. The power factor is therefore cos 90° = 0. Since real power is P = VI cosĎ, the average real power is zero. The capacitor does exchange reactive power with the source, but it does not consume average real power when ideal.
P = VI cosĎ. For a pure capacitor, Ď = −90° in the current-voltage convention, so cosĎ = 0 and P = 0. Reactive power magnitude is Q = VI.
đ Remember Points
đ Current leads voltage by 90°
đ Power factor = 0
đ Average real power = 0
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Capacitor charge is directly proportional to voltage for a constant capacitance. If the applied voltage increases, additional charge must accumulate on the plates. During this change, current flows into the capacitor. If the applied voltage later decreases, the capacitor can release charge depending on the circuit.
Q = CV. Therefore, for constant C, V ↑ → Q ↑. Also i = C(dv/dt), so current flows whenever voltage changes.
đ Remember Points
đ Q = CV
đ V ↑ → Q ↑
đ Current flows during voltage change
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Because the capacitor remains connected to a constant-voltage source, the source fixes the voltage across the plates. When the dielectric is inserted, capacitance increases by approximately the dielectric constant factor for complete filling. The source then supplies additional charge so that Q = CV remains consistent with the unchanged voltage. Thus, voltage remains constant while charge and capacitance increase.
Battery connected → V = constant. With complete dielectric insertion, C increases and Q = CV therefore increases.
đ Remember Points
đ Constant-voltage condition → V fixed
đ Dielectric insertion → C increases
đ Extra charge comes from the source
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A larger plate area provides more region for electric field lines and charge storage, increasing capacitance. Reducing the separation between plates also increases capacitance because the same voltage can be associated with a stronger electric field and more charge for a given voltage. Therefore, increasing area and decreasing spacing both increase capacitance.
C = ÎľA/d. Hence C ∝ A and C ∝ 1/d.
đ Remember Points
đ A ↑ → C ↑
đ d ↓ → C ↑
đ Îľ ↑ → C ↑
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A basic capacitor has two conducting electrodes separated by an insulating material called a dielectric. When a voltage is applied, equal and opposite charges appear on the two conductors, and an electric field is established in the dielectric region. The dielectric increases capacitance and provides insulation between the conductors.
C = ÎľA/d describes how the dielectric and geometry determine capacitance. The dielectric is essential to the capacitor structure.
đ Remember Points
đ Conductors → plates/electrodes
đ Dielectric → insulation and polarization
đ Energy → stored in electric field
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Traditional paper capacitors are made by placing paper insulation between conducting metal foils and rolling the layered structure into a compact form. Rolling provides a relatively large effective plate area in a manageable physical volume. Modern film capacitors often use plastic films rather than paper, but the traditional construction is the rolled-foil form.
Capacitance depends on effective plate area and dielectric thickness: C = ÎľA/d. Rolling the layers allows a large effective A in a compact package.
đ Remember Points
đ Paper → dielectric
đ Metal foil → electrodes
đ Rolled layers → compact large effective area
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Air-dielectric capacitors are commonly used where relatively small capacitance, stability and adjustability are useful, especially in tuning circuits. A commonly encountered range for variable air capacitors is approximately 10 pF to 400 pF, although actual ranges depend on construction and application.
For an air capacitor, C = Îľ₀A/d approximately. The relatively low permittivity of air keeps capacitance comparatively small for a given geometry.
đ Remember Points
đ Air → ξᾣ ≈ 1
đ Commonly small capacitance
đ Useful in tuning circuits
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Capacitance is defined as the amount of charge stored per unit potential difference. Therefore, C = Q/V. The SI unit obtained from coulomb per volt is the farad (F). One farad is a very large capacitance in many practical circuits, so microfarad, nanofarad and picofarad are commonly used.
C = Q/V. Therefore, 1 F = 1 C/V.
đ Remember Points
đ Capacitance → farad
đ 1 F = 1 C/V
đ Common practical units → ÎźF, nF, pF
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Use the fundamental capacitor relation Q = CV. Rearranging gives C = Q/V. Substituting Q = 2000 ÎźC and V = 200 V gives C = 10 ÎźC/V, which is numerically 10 ÎźF because 1 ÎźF/V corresponds to the required charge-voltage ratio. Therefore, the answer is 10 ÎźF.
C = Q/V = 2000 ÎźC / 200 V = 10 ÎźF.
đ Remember Points
đ Q = CV
đ C = Q/V
đ 2000 ÎźC ÷ 200 V = 10 ÎźF
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đ Detailed Explanation
Electrolytic capacitors are generally polarized. Their positive and negative terminals must be connected correctly. Reverse polarity can cause excessive leakage current, heating, gas generation, pressure buildup and, in severe cases, rupture or explosion. Paper and ceramic capacitors are generally non-polarized, although any capacitor can fail if subjected to excessive voltage or abnormal conditions.
A polarized capacitor must not be subjected to reverse voltage beyond its permitted limits. Excessive leakage produces heating and can lead to failure.
đ Remember Points
đ Observe + and − markings
đ Reverse polarity can cause heating and failure
đ Overvoltage can damage almost any capacitor
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đ Detailed Explanation
The energy stored in a capacitor is the work required to charge it from zero charge to its final charge. Since v = q/C, integrating the charging work gives W = Q²/(2C). Using Q = CV gives the familiar form W = ½CV². Thus option A is correct.
W = ½CV² = ½QV = Q²/(2C). Unit of energy is joule (J).
đ Remember Points
đ W ∝ C at constant V
đ W ∝ V² at constant C
đ Doubling V makes energy four times
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đ Detailed Explanation
The absolute permittivity of free space is denoted by Îľ₀. It is a fundamental electrostatic constant and is approximately 8.854 × 10⁻¹² F/m. It appears in equations for electric fields, capacitance and electrostatic force. The value is distinct from relative permittivity, which is dimensionless.
Îľ₀ ≈ 8.854 × 10⁻¹² F/m. Coulomb's law: F = (1/(4ĎÎľ₀))(Q₁Q₂/r²).
đ Remember Points
đ Îľ₀ → absolute permittivity
đ Unit → F/m
đ Relative permittivity of free space → 1
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đ Detailed Explanation
Relative permittivity compares the permittivity of a material with the permittivity of free space. For free space itself, Îľ equals Îľ₀. Therefore the ratio is exactly one. Relative permittivity has no unit because it is a ratio of two quantities with the same units.
ξᾣ = Îľ/Îľ₀. For free space, Îľ = Îľ₀, so ξᾣ = 1.
đ Remember Points
đ ξᾣ is dimensionless
đ Free space → ξᾣ = 1
đ Îľ = ξᾣξ₀
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đ Detailed Explanation
Electric field intensity at a point is defined as the force experienced per unit positive test charge. Since force has both magnitude and direction, electric field intensity also has magnitude and direction. Therefore, E is a vector quantity. Its SI unit can be written as N/C or equivalently V/m.
E⃗ = F⃗/Q. Therefore E has direction. SI units: N/C = V/m.
đ Remember Points
đ E = F/Q
đ Unit → N/C or V/m
đ Direction → force direction on a positive test charge
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đ Detailed Explanation
The energy stored in a capacitor is W = ½CV². Here C = 1 F and V = 4 V. Substituting gives W = ½ × 1 × 4² = ½ × 16 = 8 J. Therefore, option D is correct.
W = ½CV² = ½ × 1 × 4² = 8 J.
đ Remember Points
đ W = ½CV²
đ V = 4 V → V² = 16
đ Stored energy = 8 J
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đ Detailed Explanation
Mica capacitors have excellent electrical stability, high insulation resistance and low dielectric loss. These characteristics make mica useful in high-frequency and radio-frequency applications where stable capacitance and low loss are important. Electrolytic capacitors are generally selected for high capacitance rather than precision high-frequency operation.
High-frequency capacitor selection depends on low dielectric loss, stable capacitance and suitable parasitic parameters. Mica has traditionally performed well in these areas.
đ Remember Points
đ Mica → low dielectric loss
đ Mica → good temperature stability
đ Electrolytic → generally polarized and high-capacitance type
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đ Detailed Explanation
A capacitor bank used for power-factor correction supplies leading reactive power to compensate for lagging reactive power drawn by inductive loads. Reactive power is measured in var and, for larger installations, kVAR. Therefore, capacitor-bank ratings for power-factor correction are normally expressed in kVAR.
Reactive power Q = VI sinĎ for a single-phase system; for three-phase systems Q = √3V_LI_L sinĎ. Capacitor-bank rating → kVAR.
đ Remember Points
đ Active power → kW
đ Apparent power → kVA
đ Reactive power → kVAR
đ Capacitors supply leading reactive power
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đ Detailed Explanation
When an analog ohmmeter is connected across a capacitor, the meter initially supplies current and the capacitor charges. A healthy capacitor therefore shows a changing resistance indication that eventually becomes very high. If the final resistance remains significantly lower than expected, current is still passing through the dielectric, indicating leakage. A fully shorted capacitor would normally show very low resistance without the normal charging behavior.
A practical capacitor test observes the transient charging response. Healthy → resistance rises very high; leaky → lower final resistance; shorted → very low resistance.
đ Remember Points
đ Healthy → very high final resistance
đ Leaky → lower-than-normal final resistance
đ Shorted → very low resistance
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đ Detailed Explanation
Use Q = CV. The capacitance is 6 ÎźF and the applied voltage is 200 V. Therefore Q = 6 × 200 ÎźC = 1200 ÎźC. The answer choices confirm that the intended capacitance unit is ÎźF. If the source were interpreted as 6 mF, the result would be 1.2 C, which would not match the options.
Q = CV = 6 ÎźF × 200 V = 1200 ÎźC = 1.2 × 10⁻³ C.
đ Remember Points
đ Q = CV
đ 6 ÎźF × 200 V = 1200 ÎźC
đ 1 ÎźF = 10⁻⁶ F
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đ Detailed Explanation
For a specified capacitance and voltage rating, physical size depends on dielectric constant, dielectric thickness, electrode construction and technology. Ceramic dielectrics can have relatively high dielectric constants, allowing a required capacitance to be obtained in a smaller volume. Therefore, ceramic capacitors are generally more compact than traditional paper capacitors of comparable ratings, although actual dimensions depend on the specific component technology.
C = ÎľA/d = Îľ₀ξᾣA/d. A larger ξᾣ can provide the required capacitance with less physical area or volume for a comparable construction.
đ Remember Points
đ Ceramic → often compact
đ Higher ξᾣ → higher C for the same geometry
đ Actual size depends on voltage, construction and technology
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đ Detailed Explanation
Capacitors connected in parallel have their capacitances added directly. Let the unknown capacitor be C₂. The required equivalent is 150 pF and the existing capacitor is 50 pF. Therefore 150 = 50 + C₂, giving C₂ = 100 pF.
Parallel combination: C_eq = C₁ + C₂. Therefore C₂ = C_eq − C₁ = 150 pF − 50 pF = 100 pF.
đ Remember Points
đ Ceq = C₁ + C₂ + ...
đ 150 − 50 = 100 pF
đ Series capacitors do not add directly
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đ Detailed Explanation
For approximately identical geometry, capacitance is proportional to dielectric permittivity. Many ceramic formulations have a higher relative permittivity than mica, so ceramic can provide a larger capacitance in the same physical volume. The exact comparison depends on the specific ceramic formulation and mica type, but ceramic is the intended answer.
C = Îľ₀ξᾣA/d. With A and d approximately fixed, C ∝ ξᾣ.
đ Remember Points
đ C ∝ ξᾣ for fixed geometry
đ Ceramic can have high ξᾣ
đ Mica is especially valued for stability and low loss
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đ Detailed Explanation
Relative permittivity compares a material's permittivity with free-space permittivity. Typical approximate values are vacuum 1, many oils around 2–3, paper around 3–4, glass often around 4–10, while some ceramics can be much higher. Therefore, among the listed materials, oil generally has the lowest dielectric constant.
ξᾣ = Îľ/Îľ₀. Typical values are approximate and depend on material composition, frequency and temperature.
đ Remember Points
đ Vacuum → 1
đ Oil → typically around 2–3
đ Ceramics can have very high ξᾣ
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đ Detailed Explanation
Electrolytic capacitors are primarily designed to provide relatively large capacitance in a compact package and are commonly available at comparatively modest voltage ratings in conventional component comparisons. Mica, paper and ceramic capacitors can be manufactured for a broad range of higher-voltage applications. The exact voltage rating always depends on the component design and manufacturer.
Breakdown/working voltage depends on dielectric strength, dielectric thickness, geometry and construction. A simplified electric-stress relation is E ≈ V/d.
đ Remember Points
đ Electrolytic → high capacitance, usually polarized
đ Voltage rating depends on construction
đ E ≈ V/d describes electric stress across a uniform dielectric
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đ Detailed Explanation
Traditional paper capacitors were manufactured for moderate and relatively high voltages. A commonly quoted historical range is approximately 200 to 1600 V. The exact breakdown or working voltage depends on dielectric thickness, impregnation, construction and design. Therefore, within the choices, 200–1600 V is the intended answer.
Electric stress is approximately E = V/d for a uniform dielectric. Increasing dielectric thickness generally increases voltage withstand capability, provided the material and construction are suitable.
đ Remember Points
đ Dielectric thickness affects voltage withstand
đ Higher dielectric strength → higher breakdown voltage
đ Actual rating depends on construction
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đ Detailed Explanation
Mica has a relative permittivity typically in the approximate range of 3 to 8, depending on its type and composition. Mica is valued in capacitors not simply for its dielectric constant but also for excellent insulation, high dielectric strength, low dielectric loss and good temperature stability.
ξᾣ = Îľ/Îľ₀. For mica, the approximate relative permittivity is ξᾣ ≈ 3–8.
đ Remember Points
đ Mica → stable dielectric
đ Low dielectric loss
đ Useful for precision and high-frequency capacitors
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đ Detailed Explanation
Relative permittivity is defined as the ratio of a material's permittivity to the permittivity of free space. For vacuum, the two are identical, so their ratio is one. Relative permittivity is dimensionless because it is a ratio of two quantities with identical units.
ξᾣ = Îľ/Îľ₀. For vacuum Îľ = Îľ₀, therefore ξᾣ = 1.
đ Remember Points
đ Relative permittivity has no unit
đ Vacuum is the reference
đ Îľ = ξᾣξ₀
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đ Detailed Explanation
Electrolytic capacitors are generally polarized and are marked with positive and negative terminals. Correct polarity is essential in DC applications. Reverse connection can cause excessive leakage, heating and severe failure. Air, paper and mica capacitors are generally non-polarized and can normally be connected without a fixed polarity.
A polarized capacitor must be operated within its specified polarity and voltage limits. Reverse polarity can greatly increase leakage current.
đ Remember Points
đ Electrolytic → polarized
đ Observe + and −
đ Air/paper/mica → generally non-polarized
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đ Detailed Explanation
Certain ceramic dielectric formulations have controlled temperature coefficients of capacitance. This predictable variation can be deliberately used to compensate for temperature-dependent changes in another part of a circuit. Such capacitors are useful in oscillators, tuned circuits and precision networks where frequency or capacitance stability is important.
Temperature coefficient can be represented approximately as ÎąC = (1/C)(dC/dT), often specified in ppm/°C. A suitable positive or negative coefficient can be selected for compensation.
đ Remember Points
đ Temperature coefficient → change in C with temperature
đ Specified commonly in ppm/°C
đ Used for stability/compensation in tuned and oscillator circuits