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. \( \frac{4R}{3} \)

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

Step 1: Identify Nodes

The outer circular wire is a perfect conductor, so all points on it are at the same potential. Therefore, the left, top, bottom, and right boundary points are all the same node as B.

Let the center junction be node C. Point A is connected to C through one resistor R.

Step 2: Resistance between C and B

From the central node C to the outer node B, there are three resistors of resistance R connected:

• One resistor from C to the left boundary
• One resistor from C to the top boundary
• One resistor from C to the bottom boundary

Since all boundary points are the same node (outer wire), these three resistors are in parallel.

R_CB = R || R || R

1/R_CB = 1/R + 1/R + 1/R = 3/R

R_CB = R/3

Step 3: Total resistance between A and B

The point A is connected to C via one resistor R. Then from C to B the equivalent resistance is R/3.

These two are in series, so:

R_eq = R + R/3 = (3R + R)/3 = 4R/3