Question

What is the total resistance of n resistors each of resistance are connected in?

Answer 1

Answer:

Given:

Total "n" resistors have been provided.

To find:

Net resistance in case of parallel and series combinations.

Concept:

When we connect several resistance, we can think of another imaginary circuit where only one resistance (equal to the net resistance) has been used.

Calculation:

1st case:

Series combinations:

Net resistance = R + R + R +...... n times

=> Net resistance = n × R

=> Net resistance = nR

2nd case:

Parallel combination:

$\frac{1}{R\: eq.} = \frac{1}{R} + \frac{1}{R} + .......n \: times$

=> 1/R eq. = n/R

=> R eq. = R/n

So final answer :

Net resistance (series combination) = nR

Net resistance (parallel comb. ) = R/n

Answer 2

Answer:

Net resistance (series combination) = nR

Net resistance (parallel comb. ) = R/n