A copper wire of length and radius is connected across a fixed potential difference

PHYSICS · Single correct · A Level · Physics · Electricity · Electricity

Problem

A copper wire of length

l

and radius

r

is connected across a fixed potential difference. An aluminum wire of the same length but radius

2r

is connected to an identical potential difference. Given that the resistivities are

\rho_{\text{Cu}}=1.7\times10^{-8}\,\Omega\!\cdot\!\text{m}

and

\rho_{\text{Al}}=2.8\times10^{-8}\,\Omega\!\cdot\!\text{m}

, which statement correctly compares the rate at which thermal energy is produced in the two wires? (a)

P_{\text{Al}}\approx 1.2\,P_{\text{Cu}}

(b)

P_{\text{Al}}\approx 0.41\,P_{\text{Cu}}

(c)

P_{\text{Al}}\approx 2.4\,P_{\text{Cu}}

(d)

P_{\text{Al}}\approx 4.0\,P_{\text{Cu}}