Q 12-03-305JEE MainJEE Main 2025 (4 Apr, Shift 2)Easy
From the combination of resistors with resistance values $R_1 = R_2 = R_3 = 5\ \Omega$ and $R_4 = 10\ \Omega$, which of the combinations shown in the figure is the best circuit to get an equivalent resistance of $6\ \Omega$?
Answer: (A) Circuit (1)
Work out each circuit:
- (1) $(R_1 + R_2) \parallel (R_3 + R_4) = 10 \parallel 15 = \dfrac{10\times15}{25} = 6\ \Omega$ ✔
- (2) $(R_1 + R_2 + R_4) \parallel R_3 = 20 \parallel 5 = 4\ \Omega$
- (3) $R_1 \parallel (R_2 + R_3) \parallel R_4 = 5 \parallel 10 \parallel 10 = 2.5\ \Omega$
- (4) all four in parallel: $\left(\tfrac15 + \tfrac15 + \tfrac15 + \tfrac1{10}\right)^{-1} \approx 1.43\ \Omega$
Circuit (1) gives $6\ \Omega$.
Solution by Sreeraj P, M.Sc Physics