What is the total resistance in the following circuit element ? [Image

What is the total resistance in the following circuit element ?
[Image of a circuit diagram with three resistors labelled R. Two are in parallel, and this combination is in series with the third resistor.]

R/2
3R
3R/2
2R/3
This question was previously asked in
UPSC NDA-1 – 2023
The circuit element consists of three resistors, each with resistance R. Two of the resistors are connected in parallel, and this parallel combination is connected in series with the third resistor. To find the total resistance, we first calculate the equivalent resistance of the parallel part and then add it to the resistance of the series part.
– For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances: $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + …$
– For resistors in series, the equivalent resistance is the sum of individual resistances: $R_s = R_1 + R_2 + …$
Let the resistance of each resistor be R.
The two resistors in parallel have equivalent resistance $R_p$.
$\frac{1}{R_p} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}$.
$R_p = \frac{R}{2}$.
This parallel combination ($R_p$) is in series with the third resistor (R).
The total resistance $R_{total}$ is the sum of the series components:
$R_{total} = R_p + R = \frac{R}{2} + R = \frac{R + 2R}{2} = \frac{3R}{2}$.