Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3 Ω . Cell 2 has emf of 6 V and internal resistance of 6 Ω . An external resistor R of 4 Ω is

Question

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

TestHub · Accepted Answer

Equivalent internal resistance of two cells in parallel is $r_{e q} = \frac{r_{1} r_{2}}{r_{1} + r_{2}} = \frac{3 \times 6}{3 + 6} = 2 Ω$

Equivalent emf of given cells

$E_{e q} = (\frac{E_{1}}{r_{1}} - \frac{E_{2}}{r_{2}}) r_{e q} = (\frac{12}{3} - \frac{6}{6}) 2 = 6 V$

Given: $R = 4 Ω$

The circuit can be redrawn as shown below.

Current through resistor $R$ is $I = \frac{6}{2 + 4} = 1 A$ .

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