Question

Calculate the ratio of the equivalent resistance of the above two wires in parallel combination to that in series combination.

Answer 1

The ratio of the equivalent resistance of combination is the parallel series

Answer 2

Ratio of resistance in series to parallel = n2 : 1

Explanation:

Voltage is V and current flowing in the circuit is I. Let R1, R2.... be the resistance in a series combination.  

In a series combination:  

R (total) = R1 + R2 +....R(n)

Here R1 = R2 = R(n)

So R(series) = nR

In a parallel combination:

1 / R(total) = 1/R1 + 1/R2 +..... 1/R(n)

R1 = R2 = R(n)

So 1/R =  n/R

So R(parallel) = R/n

Ratio of resistance in series to parallel = nR /  (R/n) = n2 : 1