Question

A uniform wire of diameter \(d\) carries a current of \(100 \, \text{mA}\) when the mean drift velocity of electrons in the wire is \(v\). For a wire of diameter \(\frac{d}{2}\) of the same material to carry a current of \(200 \, \text{mA}\), the mean drift velocity of electrons in the wire is

• A. 4v
• B. 8v
• C. v
• D. 2v

Answer 1

The Correct Option is B

Current (I) = $nAv_dq_e$, where n is electron density, A is cross-sectional area, $v_d$ is drift velocity, q is the charge of an electron, and e is the electronic charge.

Since $A = \pi \left(\frac{D}{2}\right)^2 = \frac{\pi D^2}{4} \propto d^2$, we have $I \propto d^2 v_d$.

$\frac{100}{200} = \frac{d'^2 v'}{\left(\frac{d}{2}\right)^2 v'} \implies v' = 2 \times 2^2 v = 8v$