Question

calculate the ratio of equivalent resistance for a series combination of n number of identical resistors to the parallel combination of the same type of n number of resistors

Answer 1

hope it helps you to understand better

Answer 2

Given : n resistors

To find : ratio of equivalent resistance for a series combination  to parallel

Explanation:

For the series combination

Equivalent resistance of n resistors are

$(R_e_q)_1= nR$

For parallel combination

Equivalent resistance of n resistors are

$\frac{1}{(R_e_q)_2}= \frac{1}{R}+ \frac{1}{R}+ \frac{1}{R}...n\\\\\frac{1}{(R_e_q)_2}=\frac{n}{R}\\\\therefore\\\\(R_e_q)_2= \frac{R}{n}$

thus ratio is

$\frac{(R_e_q)_1}{(R_e_q)_2}= \frac{nR\times n}{R}\\\\\frac{(R_e_q)_1}{(R_e_q)_2}=n^2$