Question 186 of 380

In the given figure, a battery of emf $E$ is connected across a conductor $PQ$ of length $l$ and different area of cross-sections having radii ${r}_{1}$ and ${r}_{2}\left({r}_{2}\lt {r}_{1}\right).$

Choose the correct option as one moves from $P$ to $Q$.

ADrift velocity of electron increases.BElectric field decreases.CElectron current decreases.DAll of these

Show answer and solution▾

Answer: (A) Drift velocity of electron increases.

Current is constant in conductor
$i=$constant
Resistance of element $dR=\dfrac{\rho dx}{\pi {r}^{2}}$
$dV=idR=\dfrac{\text{ipdx}}{\pi {r}^{2}}$
$E=\dfrac{dV}{dx}=\dfrac{i\rho }{\pi {r}^{2}}$
and ${V}_{d}=\dfrac{eE\tau }{m}$
$∴{V}_{d}\times E$
$\rightarrow E\propto \dfrac{1}{{r}^{2}}$
If $r$ decreases, $E$ will increase.
$∴{V}_{d}$ will increase.