Question

Household wiring often uses 2.0-mm-diameter copper wires. The wires can get rather long as they snake through the walls from the fuse box to the farthest corners of your house. You may want to review (Pages 755 - 759) . Part A What is the potential difference across a 18-m-long, 2.0-mm-diameter copper wire carrying an 7.5 A current? Express your answer to two significant figures and include the appropriate units.

Answer 1

Resistivity of copper wire ρ = (1.68×10^-8) Ohm-m

Total resistance (R) of a wire having length L and diameter D is given by

R= (resistivity x L) / A

R= (ρL) / A

Given: L =18m = , D = 2 mm = 2×10^-3 m

A= π x (D/2)2

A= π x (D2/4)

Total resistance of a wire

R = (4ρL) / (πD2)

= 4(1.68×10^-8)(18) / π(2×10^-3)2

= (120.96×10^-8) / (3.14 x 4 x 10^-6)

= (120.96×10^-8) / (12.56 x 10^-6)

= 9.63 ×10^-2 Ohm

= 0.0963 Ohm

Potential difference across the wire is given by

V = I x R

Current I = 7.5 A

Resistance R = 0.0963 Ohm

V = 7.5 x 0.0963

V = 0.72 Volts