Find the net resistance in the following cases.
A single strand of wire has a resistance of 5.60μΩ. 120 strands of wire are:
(a) placed side by side to form a cable of the same length as a single strand.
(b)connected end to end to form a wire 120 times the length of a single strand of wire.
When two resistors with resistances R1 and R2 are connected in series the net resistance is equal to Rn = R1 + R2. And when the two resistors are connected in parallel the net resistance is given by 1/Rn = 1/R1 + 1/R2.
a. We have 120 resistors of 5.6 micro ohm in parallel. The net resistance will be (5.6*10^-6) ^120/ 120*5.6*10^-6
= (5.6*10^-6) ^119/ 120 ohm
b. We have 120 resistors of 5.6 micro ohm connected in series. The net resistance is 120*5.6*10^-6
= 672*10^-6 ohm
We can see that when the wires are connected in parallel the net resistance is a tiny fraction of what it is when are connected in series.