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Physics · 2026 · 3 marks
CBSE 2026 · Region 3 · Set 1 · Q22
(a) Establish the relation between drift velocity of electrons ( v_d ) and electric current (I) in a conductor. (b) How is v_d affected when the…
(a)
Establish the relation between drift velocity of electrons $\displaystyle \left(\mathrm{v}_{\mathrm{d}}\right)$ and electric current (I) in a conductor.
(b)
How is $\displaystyle \mathrm{v}_{\mathrm{d}}$ affected when the length of the conductor is doubled, keeping the voltage applied across the conductor constant ?
Marking-scheme solution
(a)
For '$\displaystyle n$' number of free electrons per unit volume in a conductor of cross-section area A, the total charge transported across the area in time $\displaystyle \Delta \mathrm{t}$ is $\displaystyle Q=-n e A \mathrm{v}_{\mathrm{d}} \Delta \mathrm{t}$
As electrons move in a direction opposite to that of the electric field: $\displaystyle \mathrm{I} \Delta \mathrm{t}=n e A \mathrm{v}_{\mathrm{d}} \Delta \mathrm{t}$
$\displaystyle \mathrm{I}=A n e \mathrm{v}_{\mathrm{d}}$
(b)
$\displaystyle \mathrm{v}_{\mathrm{d}}=\dfrac{e V \tau}{m l}$
Length is doubled, so drift velocity is halved.
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