5 resistors each of the same value R are connected between points A and B as shown below. Select the correct value of equivalent resistance between points A and B.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{3}{8}R \)
Resistors in series add, and for resistors in parallel the reciprocals add.
The network in the figure reduces to three branches in parallel between A and B: two single resistors \( R \), and a branch of \( R \) in series with a parallel pair of \( R \).
The parallel pair and its series resistor:
\( \displaystyle R \parallel R = \frac{R}{2} \qquad R + \frac{R}{2} = \frac{3R}{2} \)
The two single resistors together:
\( \displaystyle R \parallel R = \frac{R}{2} \)
The two results in parallel:
\( \displaystyle R_{AB} = \frac{\frac{R}{2} \times \frac{3R}{2}}{\frac{R}{2} + \frac{3R}{2}} = \frac{3R^{2}/4}{2R} = \frac{3}{8}R \)