A strand of wire has resistance$\mathbf{5}\mathbf{.}\mathbf{60}\mathbf{}\mathit{m}\mathit{\Omega }$.Find the net resistance of 120such strands if they are

(a) placed side by side to form a cable of the same length as a single strand, and

(b) connected end to end to form a wire 120times as long as a single strand.

Now, according to the relation between the resistance, the area, and the length, we know that the resistance is inversely proportional to the area where as the resistivity and the length are constant.

Thus, when the area increases by the factor 120, the resistance will decrease by the same factor and the net resistance will be

$R_{120}=\frac{R}{120}=\frac{5.60}{120}=0.047\mu \Omega$

Therefore, the net resistance of 120 strands if they are placed side by side to form a cable of the same length as a single strand is $0.047\mu \Omega$

According to the relation between the resistance, the area, and the length we know that the resistance is directly proportional to the length.

Thus, when the length of the wires increases by the factor 120 , the resistance will increase by the factor 120 and the net resistance will be

$R_{120}=120R=120\left(5.60\right)=672\mu \Omega$

Therefore, the net resistance of 120 strands if they are connected end to end to form a wire 120 times as a single strand is$672\mu \Omega$