Question

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.

Short answer

(a) The net resistance of 120 strands if they are placed side by side is$0.047\mu \Omega$

(b) The net resistance of 120 strands if they are connected to end to end form is$672\mu \Omega$

Step-by-step solution

Determine the net resistance of 120 strands if they are placed side by side

(a) If we connect 120 strands side by side, the length of the wires will be same but the area will, which will increase by the factor 120.

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 $0.047\mu \Omega$

Determine the net resistance of 120 strands when connected end to end

(b) If we connect 120 strands end to end, the area of the wires will be the same but in this case the length will change, which will increase by the factor 120.

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$672\mu \Omega$