Answer to Question #85510 in Electric Circuits for James

Question

What current flows through a 2.54- cm diameter rod of pure silicon that is 20.0
cm long, when 1.00× 103 ?

Answer 1

I guess that the voltage is 1000=10^3 V, not 103 V.

First, find the resistance of the rod with cross-sectional area $A$, length $L$, and resistivity $\rho$:

$$R=\frac{\rho L}{A}=\rho L\cdot \frac{4}{\pi D^2}.$$

According to Ohm's law the current is

$$I=\frac{V}{R}=\frac{\pi VD^2}{4\rho L}=\frac{3.14\cdot 10^3\cdot 0.0254^2}{4\cdot 0.2\cdot 2300}=1.1\cdot 10^{-3}\text{ A},$$

or 1.1 mA