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?
Solution.
R=ρlS;R=\rho\dfrac{l}{S};R=ρSl;
l1=2l;l_1=2l;l1=2l;
d1=2d;d_1=2d;d1=2d;
S=πd24;S=\pi \dfrac{d^2}{4};S=π4d2;
S1=π4d24=πd2=4S;S_1=\pi\dfrac{4d^2}{4}=\pi d^2=4S;S1=π44d2=πd2=4S;
R1=ρ2l4S=ρl2S=R2=12R;R_1=\rho\dfrac{2l}{4S}=\rho\dfrac{l}{2S}=\dfrac{R}{2}=\dfrac{1}{2}R;R1=ρ4S2l=ρ2Sl=2R=21R;
Answer:12R.\dfrac{1}{2}R.21R.
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