A. The drift velocity of electrons decreases | vedclass

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(B) The drift velocity $v_d$ is given by the formula: $v_d = \frac{e 	au E}{m} = \frac{e 	au}{m} \left( \frac{\Delta V}{\ell} ight)$.$1$. Effect o

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$A$ and $D$ only

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(B) The drift velocity $v_d$ is given by the formula: $v_d = \frac{e 	au E}{m} = \frac{e 	au}{m} \left( \frac{\Delta V}{\ell} ight)$.$1$. Effect of temperature: As temperature increases,the collision frequency of electrons increases,which causes the relaxation time $	au$ to decrease. Since $v_d \propto 	au$,the drift velocity decreases. Thus,statement $A$ is correct and $E$ is incorrect.$2$. Effect of length: From the formula $v_d = \frac{e 	au \Delta V}{m \ell}$,it is clear that $v_d \propto \frac{1}{\ell}$. Thus,statement $D$ is correct.$3$. Effect of area: The drift velocity is related to current by $I = n e A v_d$. If the current $I$ is constant,then $v_d = \frac{I}{n e A}$,implying $v_d \propto \frac{1}{A}$. However,in a general conductor where potential difference $\Delta V$ is fixed,$v_d = \frac{e 	au \Delta V}{m \ell}$,which is independent of the cross-sectional area $A$. Thus,statement $B$ is incorrect.$4$. Effect of potential difference: Since $v_d = \frac{e 	au \Delta V}{m \ell}$,the drift velocity is directly proportional to the applied potential difference $\Delta V$. Thus,statement $C$ is incorrect.Therefore,statements $A$ and $D$ are correct.

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