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. R
• B. 2R
• C. 3R/2
• D. 2R/3

Answer 1

Answer: (D)

2R/3

Answer 2

When the key K is open, the branch containing resistor R4 and the key K is disconnected from the circuit. The circuit then simplifies to two parallel branches between points A and B.

Branch 1: Consists of resistor R1 and R3 connected in series. The equivalent resistance of this branch is $R_1 + R_3 = R + R = 2R$.

Branch 2: Consists of resistor R2. Since the path through R4 is open, this branch directly connects A to B (or Q is effectively connected to B in a way that R2 is the only resistance in this path between A and B). The resistance of this branch is $R_2 = R$.

These two branches are in parallel. The equivalent resistance ($R_{AB}$) between A and B is calculated as: $R_{AB} = \frac{(R_1 + R_3) \times R_2}{(R_1 + R_3) + R_2}$ Substituting the values: $R_{AB} = \frac{(2R) \times R}{2R + R} = \frac{2R^2}{3R} = \frac{2R}{3}$