Question

Four resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open will be:

• A. \( 4R \)
• B. \( \infty \)
• C. \( \frac{R}{4} \)
• D. \( \frac{3R}{2} \)

Hint:

When dealing with resistors in series and parallel, simplify the circuit step by step. First, combine resistors in series or parallel, then combine the resulting resistances. This method makes the problem easier to solve.

Answer 1

The Correct Option is D

When key $K$ is open, we observe that the resistors form a combination of series and parallel resistances. The two resistors connected between points $A$ and $B$ are in parallel, and the other two resistors are in series with this parallel combination.
1. The two resistors between $A$ and $B$ are in parallel, so their equivalent resistance is given by: \[ R_{\text{eq}} = \frac{R}{2} \] 2. This equivalent resistance is in series with the other resistor $R$, so the total equivalent resistance becomes: \[ R_{\text{total}} = R + \frac{R}{2} = \frac{3R}{2} \] Thus, the equivalent resistance between points $A$ and $B$ when key $K$ is open is \( {\frac{3R}{2}} \).