Question

There are m resistor each of resistance R . First they all are connected in series and equivalent resistance is X . Now they are connected in parallel and equivalent resistance is Y . What is the ratio of X and Y ?

Answer 1

Solution :-

First case :

m resistors of RΩ resistance are connected in series.

Equivalent resistance = X

Equivalent resistance of series connection :

X = R₁ + R₂ + ... + Rₙ

X = R + R + ... + R

X = mR ... (i)

Second case :

m resistors of RΩ resistance are connected in parallel.

Equivalent resistance = Y

Equivalent resistance of series connection :

1/Y = 1/R₁ + 1/R₂ + ... + 1/Rₙ

1/Y = 1/R + 1/R + ... + 1/R

1/Y = m/R

Y = R/m ... (ii)

Taking ratio,

X/Y = mR/(R/m)

X : Y = m² : 1