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. 4R
• C. 2R
• D. R/2

Answer 1

Answer: (A)

R

Answer 2

Assuming the standard Wheatstone bridge configuration with four resistors of resistance R and the key K in the diagonal. The bridge is balanced ($\frac{R}{R} = \frac{R}{R}$). When the bridge is balanced, no current flows through the diagonal element (key K). Therefore, the equivalent resistance between A and B is independent of the state of key K. The resistance of each parallel branch (A-C-B and A-D-B) is $R+R = 2R$. The equivalent resistance is the parallel combination of two $2R$ branches: $R_{eq} = (2R || 2R) = \frac{2R \times 2R}{2R + 2R} = R$.