Question

A 13-m of wire is constructed such that half of its length is copper, and the other half is aluminum. The diameter of the wire is 1.52 mm. Determine the total resistance of the wire. Express your answer in milliohms.

B)

If a voltage difference of 85.9 mV is placed across the wire, determine the current through the wire.

Answer 1

Resistivity of copper, c = 1.68 x 10^-8 ohm m
Length, L = 6.5 m
Area, A = r²
= x (0.76 x 10^-3)² = 1.81 x 10^-6 m².
Resistance, Rc = cL/A
= [(1.68 x 10^-8) x 6.5] / (1.81 x 10^-6)
= 60.18 m

Resistivity of aluminum, a = 2.65 x 10^-8 ohm m
Length, L = 6.5 m
Area, A = r²
= x (0.76 x 10^-3)² = 1.81 x 10^-6 m².
Resistance, Ra = aL/A
= [(2.65 x 10^-8) x 6.5] / (1.81 x 10^-6)
= 94.93 m

Since these resistors are in series,
Net resistance, R = Rc + Ra
= 60.18 m + 94.93 m
= 155.1 m

b)
Current, I = V/R
= 85.9 mV / 155.1 m
= 0.554 A