Question

What current flows through a 2.62 cm diameter rod of pure silicon that is 23.5 cm long, when 1000 v is applied to it? (such a rod may be used to make nuclear particle detectors, for example.) the resistivity of pure silicon is 2.30 103 ω · m?

Answer 1

Resistivity = resistance * Area / Length
resistance = ??
rho = 2.30 * 10^3 ohms meters.
l = 23.5 cm = 0.235 meters.
diameter = 2.62 cm = 0.0262 m
Radius = diameter / 2 = 0.0131 m
Area = pi r^2 where pi = 3.14
Area = 3.14 * 0.0131^2 = 0.000539 m^2

2.30 * 10^3 = R * 0.000539 /0.235
2.30 * 10^3 * 0.235/0.000539 = R
R = 1002783 which is about 1 meg ohm, but I'll use the calculation here.

E = 1000 V
R = 1 002 783 ohms
I = ???

E = I * R
1000 = I * 1002783 We should really round that resistor to 1 megohm or 1 * 10^6 ohms.

I = 1*10^3 / 1 * 10^6
I = 1 * 10^-3 amp = 1 milliamp. Pretty reasonable all things considered.