CBSE 2023 · Region 2 · Set 3 · Q29 · 3 marks
A potential difference V is applied across a conductor of length $\displaystyle l$ 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,(b)the conductor were gradually stretched to reduce its cross-sectional area to $\displaystyle \frac{\mathrm{A}}{2}$ and then the same potential difference V is applied across it.
A potential difference V is applied across a conductor of length $\displaystyle l$ 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,
(b)
the conductor were gradually stretched to reduce its cross-sectional area to $\displaystyle \frac{\mathrm{A}}{2}$ and then the same potential difference V is applied across it.
Marking-scheme solution
(a)
Current density $\displaystyle j = \dfrac{ne^2 E\tau}{m}$
$\displaystyle = \dfrac{ne^2 V\tau}{ml}$
Or $\displaystyle j \propto V$
If $\displaystyle V$ is doubled, the current density will be doubled.
(b)
As the conductor were gradually stretched to reduce its cross sectional area to half $\displaystyle (A/2)$, its length will become double $\displaystyle (2l)$ as volume of conductor remains the same.
$\displaystyle \because\ j \propto \dfrac{1}{l}$
$\displaystyle \therefore$ If same potential difference is applied, the current density will become half.
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