Question

A potential difference of V volt Is applied to a conductor of length L and diameter D. How are the electric field Eand resistance of the conductor affected when in turn? i.) V is doubled

Answer 1

Answer:

Electric Field, E=

length of the conductor, L

potential difference, V

.

Hence, the electric field is directly proportional to potential difference and inversely proportional to the length of the conductor.

And, Resistance, R=

area of the cross section, A

Resistivity × length of the conductor, L

Hence, the resistance is directly proportional to the length of the conductor and inversely proportional to the area f cross section.

And, area of cross section can be written as A=

4

πD

2

Hence area of cross section is directly proportional to the square of the diameter of the conductor.

Case 1: when V is halved

As V and E are directly proportional to each other, E is halved.

On halving the voltage, the current will also get halved, and by Ohm's law V=IR, such that R will remain unchanged.

Case 2: L is halved

As L and E are inversely proportional to each other, E will get doubled.

And as L and R are directly proportional to each other, R will get halved.

Case 3: D is doubled

As E is independent of the area of cross-section, so E will remain unchanged.

Resistance is inversely proportional to area of cross-section and area of cross-section is directly proportional to the square of the diameter of the conductor, hence resistance is inversely proportional to square of the diameter of the conductor.

hence when D is doubled, area of cross section will become 4 times more, and resistance will become (

4

1

)

th

times the original.