Question

Four resistors, each of resistance $ R $, are connected as shown in the figure below.

• A. The total resistance between points 1 and 3 is 0.5 R.
• B. The total resistance between points 1 and 6 is 3.5 R.
• C. The total resistance between points 3 and 6 is 2 R.
• D. The total resistance between points 2 and 4 is 0.5 R.

Hint:

To simplify circuits with resistors in parallel, use the formula \( \frac{R_1 R_2}{R_1 + R_2} \). For resistors in series, simply add the resistances.

Answer 1

The Correct Option is D

In this circuit, the resistors are connected in a combination of series and parallel. 
Let's break it down: 
- Resistors between points 1 and 6 are in series, so the total resistance between points 1 and 6 will be the sum of the resistances of the two resistors connected in series: \[ R_{\text{total between 1 and 6}} = R + R = 2R \] 
- Resistors between points 3 and 6 are in parallel. The equivalent resistance \( R_{\text{eq}} \) for two resistors \( R \) in parallel is given by: \[ R_{\text{eq}} = \frac{R \times R}{R + R} = \frac{R}{2} \] - The total resistance between points 2 and 4 is the parallel combination of two resistors each of resistance \( R \): \[ R_{\text{total between 2 and 4}} = \frac{R}{2} \] 
Thus, the total resistance between points 2 and 4 is \( 0.5R \).