If two resistors of value R are connected in series and then in parallel, what is the difference in equivalent resistance in both cases?

Given: Two resistors of value R are connected in series and then in parallel

To find: Difference in equivalent resistance in both cases

Solution:

Series case:

Effective Resistance = R₁ + R₂

= R + R

So effective resistance = 2R

Parallel case:

We can find effective resistance using the formula

$\frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2}$

$\frac{1}{R_{eff}} = \frac{1}{R} + \frac{1}{R}$

$\frac{1}{R_{eff}} = \frac{2}{R}$

So effective resistance, $R_{eff} = \frac{R}{2}$

Difference:

The difference is $2R - \frac{R}{2} = \frac{3R}{2}$