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/2
• B. R
• C. 2R
• D. 4R

Answer 1

Answer: (B)

R

Answer 2

When the key K is open, the circuit can be analyzed as two parallel branches connecting points A and B.

Branch 1 (A-C-B): This branch consists of two resistors of resistance R in series, so the total resistance is $R + R = 2R$.

Branch 2 (A-D-B): This branch also consists of two resistors of resistance R in series, so the total resistance is $R + R = 2R$.

These two branches are connected in parallel between points A and B. The equivalent resistance ($R_{eq}$) of two parallel resistors is given by: $R_{eq} = \frac{R_1 \times R_2}{R_1 + R_2}$ Substituting the resistances of the two branches: $R_{eq} = \frac{(2R) \times (2R)}{(2R) + (2R)} = \frac{4R^2}{4R} = R$ Therefore, the equivalent resistance between points A and B when key K is open is R.