A uniform wire of diameter $d$ carries a current of 100 mA when the mean drift velocity of electrons

Question

A uniform wire of diameter $d$ carries a current of 100 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 mA , the mean drift velocity of electrons in the wire is

Professor PC Thomas Classes · Answer

(b) : As we know, $I=n A e v_d$ where, $I=100 \mathrm{~mA}$, diameter $=d$ and $v_d=v 100 \mathrm{~mA}=n A e v$ Now, $I=200 \mathrm{~mA}$, diameter $=\frac{d}{2}$ and $v_d=v^{\prime}$ $ \ 200 \mathrm{~mA}=n A^{\prime} \mathrm{ev}^{\prime} $ From equation (i) and (ii) \ $ \frac{100}{200}=\frac{n A e v}{n A^{\prime} e v^{\prime}} ; \frac{1}{2}=\frac{\pi 	imes d^2 / 4 	imes v}{\pi 	imes d^2 / 16 	imes v^{\prime}} ; \frac{1}{2}=\frac{4 v}{v^{\prime}} \Rightarrow v^{\prime}=8 v $