In the circuit shown in figure, a $12 V$ battery with unknown internal resistance $r$ is connected to another battery with unknown emf $E$ and internal resistance $1 Ω$ and to a resistance of $3 Ω$ carrying a current of $2 A$ . The current through the rechargeable battery is $1 A$ in the direction shown. Find the unknown current $i$ , internal resistance $r$ and the emf $E$ .

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$i = - 3 A$

$E = 5 V, r = 2 Ω$

$i = 3 A$

$E = - 5 V, r = 5 Ω$

$i = 3 A$

$E = - 5 V, r = 2 Ω$

$i = 8 A$

$E = 5 V, r = 2 Ω$

answer is D.

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Detailed Solution

Applying loop law equation in upper loop, we have

$E + 12 - i r - 1 = 0$

Applying loop law equation in lower loop, we have where

$i = 1 + 2 = 3 A$

$E + 6 - 1 = 0$

Solving these two equations, we get

$E = - 5 V and r = 2 Ω$

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