Question

A copper wire having length L and diameter d has risistance R. What will the resistance be of a copper wire with length 2L and diameter 2d?

Answer 1

Solution.

$R=\rho\dfrac{l}{S};$

$l_1=2l;$

$d_1=2d;$

$S=\pi \dfrac{d^2}{4};$

$S_1=\pi\dfrac{4d^2}{4}=\pi d^2=4S;$

$R_1=\rho\dfrac{2l}{4S}=\rho\dfrac{l}{2S}=\dfrac{R}{2}=\dfrac{1}{2}R;$

Answer:$\dfrac{1}{2}R.$