(a) area is reduced
(b) length is reduced
(c) length is increased
(d) length increased and area reduced
Correct Answer: (b) length
is reduced
Explanation
Reducing length reduces resistance, increasing
current.
Notes for
More Information
Relation Between Current,
Resistance, and Length of Conductor
1. According
to Ohm’s law, for a fixed supply voltage (V), the current
(I) flowing through a conductor is inversely proportional to
its resistance (R).
2. Mathematically:
Dependence of Resistance on
Length and Area
3. The
resistance of a conductor is given by:
4. Where:
·
= resistivity of the
material
·
= length of the conductor
·
= cross-sectional area of
the conductor
5. From this
equation:
·
Resistance is directly proportional to length (L).
·
Resistance is inversely proportional to cross-sectional area (A).
Effect on Current
6. To increase
the current, the resistance must be reduced.
7. When
the length of the conductor is reduced, electrons travel a shorter
path.
8. This
results in fewer collisions with atoms, thereby reducing
resistance.
9. Lower
resistance allows more current to flow for the same applied
voltage.
Effect of Increasing Length
10.
If the length of the conductor is increased:
·
Resistance increases.
·
Current decreases for a fixed voltage.
11.
Therefore, increasing length reduces current flow.
Explanation Using Ohm’s Law
12.
Ohm’s law is:
13.
For a constant voltage:
14.
Hence:
·
If R decreases, I increases.
·
If R increases, I decreases.
Conclusion
15.
Resistance is directly proportional to the length of
the conductor.
16.
Reducing the length reduces resistance and increases
current.
17.
Increasing the length increases resistance and reduces
current.