Question

A 14.0 gauge copper wire of diameter 1.628 mm carries a current of 10.0 mA .

a)What is the potential difference across a 2.00 m length of the wire?

b)What would the potential difference in part A be if the wire were silver instead of copper, but all else was the same?

Answer 1

Assuming: resistivity at room temp:
p_copper = 1.72*10^-8 ohm-m
p_silver = 1.47*10^-8 ohm-m

D = 0.001628 m
I = 0.010 A
L = 2 m
A = pi (D/2)² = 2.08x 10^-6 m²

R = ρ L / A
R_copper = p_copper * L / A = 1.65 x 10^-2 ohms
R_silver = p_silver * L / A = 1.41x 10^-2 ohms

Answers:
a)potential difference across a 2.00 m length of the wire

V_copper = i*Rc = 1.65 x 10^-4 V

B)potential difference if the wire were silver instead of copper

V_silver= i*Rs= 1.41 x 10^-4 V