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
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2023
– For resistors in series, the equivalent resistance is the sum of individual resistances: $R_s = R_1 + R_2 + …$
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:
$R_{total} = R_p + R = \frac{R}{2} + R = \frac{R + 2R}{2} = \frac{3R}{2}$.