Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of $3\Omega$. Cell 2 has emf of 6 V and internal resistance of $6\Omega$. An external resistor R of $4\Omega$ is connected across A and B. The current flowing through R will be ____ A.

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Current Electricity

Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of

3Ω

. Cell 2 has emf of 6 V and internal resistance of

6Ω

. An external resistor R of

4Ω

is connected across A and B. The current flowing through R will be ____ A.

Answer: 1

The two branches between A and B carry cells with opposing emfs, so the pair acts as a single source whose emf is

E_{eq} = \frac{E _{1} / r _{1} - E _{2} / r _{2}}{1/ r _{1} + 1/ r _{2}} = \frac{12/3 - 6/6}{1/3 + 1/6} = 6 V

with internal resistance

r_{eq} = \frac{r _{1} r _{2}}{r _{1} + r _{2}} = \frac{3 \times 6}{9} = 2 Ω

. Driving the

4 Ω

resistor, the current is

i = \frac{E _{eq}}{r _{eq} + R} = \frac{6}{2 + 4} = 1 A

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer