Question

The equivalent resistance between the points X & Y of the circuit shown below is _____ \(\Omega\).

• A. \( \frac{1}{3}R \)
• B. \( \frac{3}{2}R \)
• C. \( (2 \times 3)R \)
• D. \( (2 + 3)R \)

Hint:

To find the equivalent resistance of resistors in series and parallel, remember: - For parallel: \( \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \) - For series: \( R_{\text{eq}} = R_1 + R_2 \)

Answer 1

The Correct Option is A

The given circuit consists of resistors arranged in a combination of series and parallel.
Let's analyze the circuit step by step:
1. The two resistors \( R \) are in parallel. The equivalent resistance \( R_{\text{eq1}} \) of two resistors in parallel is given by:
\[ R_{\text{eq1}} = \frac{R}{2} \] 2. This equivalent resistance is in series with resistor \( P \), so the total equivalent resistance \( R_{\text{eq}} \) of the circuit is:
\[ R_{\text{eq}} = R_{\text{eq1}} + P = \frac{R}{2} + R = \frac{3R}{2} \] Thus, the equivalent resistance between points X and Y is \( \frac{3R}{2} \), which is option (2).