What current flows through a 2.60-cm-diameter rod of pure silicon that is 20.5 cm long, when 1.00 ✕ 103 V is applied to it? (Such a rod may be used to make nuclear particle detectors, for example.)

1.13 mA

Explanation:

Length of wire L = 20.5 cm = 0.205m

Radius of wire r = 2.60/2 = 1.3cm = 0.0130m

Voltage V = 1 * 10³ V

Resistivity of pure silicon p = 2300 Ohms • m

Cross sectional area of the wire

A = pi * r² = pi * (0.013) ² = 5.307 * 10 ^-4 m²

Resistance of the material

R = p• L/A

= 2300 • 0.205/5.307 * 10^-4 = 0.888 * 10⁶ Ohms

Using Ohms Law

R = V / I

I = V/R

I = 10³/0.888 * 10⁶

= 0.001126 A

= 1.13 mA