Q:
A potential difference V is a applied across a conductor of length / and cross-sectional area A. Briefly explain how
the current density J, in the conductor will be affected if.
(i) The potential difference V is doubled
(ii) The conductor were gradually stretched to reduce its cross-sectional area to
A/2
then same potential difference V is applied across it.
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Answer:
answer given below.
Explanation:
The resistance of a conductor of length l and cross-sectional area A is
[tex]R=\rho\frac{l}{A}[/tex]
where [tex]\rho[/tex] is the resistivity of the material.
So the current in the conductor is
[tex]I=\frac{V}{R} =\frac{V}{\rho(\frac{l}{A}) }[/tex]
and the current density is
[tex]J=\frac{I}{A} =\frac{V}{\rho(\frac{l}{A} )A} =\frac{V}{\rho l}[/tex]
(i) If the potential difference is doubled, the current density is
[tex]J'=\frac{2 V}{\rho l} =2J[/tex]
Thus, the current density is doubled.