A potential difference V is applied across a ...

CBSE Class 12 Physics 2023 Outside Delhi Set 3 Paper

Question : 12 of 13

Marks: +1, -0

A potential difference

V

is applied across a conductor of length

l

and cross-sectional area A. Briefly explain how the current density

j

in the conductor will be affected if

(a) the potential difference

V

is doubled. reduce

(b) the conductor were gradually stretched to its cross- sectional area to

\;\frac{A}{2}

and then the same potential difference

V

is applied across it.

Solution: 👈: Video Solution

Initial current

=I=\;\frac{V}{R}=\;\frac{V}{\rho \cdot \; \frac{L}{A}}=\;\frac{V A}{\rho L}

Initial current density

=J=\;\frac{V}{\rho L}

(a) Final current density

=J'=\;\frac{2V}{\rho L}=2J

So the current density becomes double.

(b) When area of cross section becomes

\;\frac{A}{2}

The length becomes

2L

So, final current density

=J''=\;\frac{V}{\rho L'}

J''=\;\frac{V}{2\rho L}=\;\frac{1}{2}J

So, the current density becomes half

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