Question

(a) A potential difference 'V' exists across a
conductor of length 'l' and cross-section area
'A'. How is the resistance 'R' of the conductor
affected when
(1) only 'V' is halved?
(ii) only 'l is halved?/
(iii) only 'A' is halved?
.
eubled on it​

Answer 1

i) resistance will be doubled

2) resistance will be halved

3=) resistance will doubled

Answer 2

Electric Field, E= V/L

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= resistiviy xL/A

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= πD ^2/4

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 (1/4) th times the original.

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