Question

A wire M of diameter d is joint to another wire N of the same material. The diameter of N is half that of M but the two wires have the same length, If a steady potential difference is applied across the ends of the composite wire, which of the following statements is correct?

A. The current in N is half of the current in M

B. The drift velocity of the electrons in N is four times that of the electrons in M.

C. The number of charge carriers per unit length in M is twice that in N

D. The drift velocity of the electrons in M is twice that of the electrons in N

Answer 1

drift velocity of the electrons:

$v = \frac{I}{enS}$

$I_N=I_M=I(\text{since the serial connection of the conductors})$

$v_N= \frac{I}{enS_N}$

$v_M= \frac{I}{enS_M}$

$\frac{v_N}{v_M}= \frac{S_M}{S_N};$

$\frac{S_M}{S_N}= \frac{\pi\frac{d_M^2}{4}}{\pi\frac{d_N^2}{4}}=4$

$\frac{v_N}{v_M}=4$

$\text{Answer: }$B. The drift velocity of the electrons in N is four times that of the electrons in M.