# Chapter 18 - Problems - Page 698: 14

$u_1 = 4~u_2$

#### Work Step by Step

We can write an expression for the drift velocity: $v_d = \frac{I}{n~q~A} = \frac{I}{n~q~\pi~r^2}$ $I$ is the current $n$ is the number of electrons per unit of volume $q$ is the charge of one electron $A$ is the cross-sectional area $r$ is the cross-sectional radius We can write an expression for the drift speed $u_1$: $u_1 = \frac{I}{n~q~\pi~r_1^2}$ We can find an expression for the drift speed $u_2$: $u_2 = \frac{I}{n~q~\pi~r_2^2}$ $u_2 = \frac{I}{n~q~\pi~(2r_1)^2}$ $u_2 = \frac{1}{4} \times \frac{I}{n~q~\pi~r_1^2}$ $u_2 = \frac{1}{4} \times u_1$ $u_1 = 4~u_2$

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