From the combination of resistors with resistance values \(\mathrm{R}_{1}=\mathrm{R}_{2}=\mathrm{R}_{3}=5 \Omega\) and \(\mathrm{R}_{4}=10 \Omega\), which of the following combination is the best circuit to get an equivalent resistance of \(6 \Omega\) ?

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Current Electricity

From the combination of resistors with resistance values

R_{1} = R_{2} = R_{3} = 5Ω

and

R_{4} = 10Ω

, which of the following combination is the best circuit to get an equivalent resistance of

6Ω

Answer: (A)

With the upper branch carrying

R_{1}

and

R_{2}

in series, its resistance is

5 + 5 = 10 Ω

, and the lower branch carrying

R_{3}

and

R_{4}

in series gives

5 + 10 = 15 Ω

. These two branches connect the same pair of terminals, so they are in parallel and the equivalent resistance is

\frac{10 \times 15}{10 + 15} = \frac{150}{25} = 6 Ω

. The circuit that places

R_{1}, R_{2}

in series in one branch and

R_{3}, R_{4}

in series in the parallel branch gives the required

6 Ω

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Single correct option