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

\;{A}/{2}

and then the same potential difference

{\V}

is applied across it.

Solution:

Initial current

=I=\;{V}/{R}=\;{V}/{ρ ⋅ \;{L}/{A}}=\;{V A}/{ρ L}

Initial current density

=J=\;{V}/{ρ L}

(a) Final current density

=J^{'}=\;{2 V}/{ρ L}=2 J

So the current density becomes double.
(b) When area of cross section becomes

\;{A}/{2}

,
The length becomes

2 {\L}

.
So, final current density

=J^{' '}=\;{V}/{ρ L^{'}}

J^{' '}=\;{V}/{2 ρ L}=\;{1}/{2} J

So, the current density becomes half

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