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Two batteries $E_{1} {and E}_{2}$ having emfs of 6V and 2V respectively and internal resistance of $2 Ω and 3 Ω$ respectively are connected in parallel across a $5 Ω$ resistor calculate.
i) Current through each battery
ii) Terminal voltage

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1.23A, 3.55 V

1A, 5V

0.33 A, 3.3 V

0.5A, 7.3 V

answer is A.

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Detailed Solution

Consider the loop HBCDEGH
Apply KVL
$\begin{array}{l} 2 i_{1} - 6 + 2 - 3 i_{2} = 0 \\ \Rightarrow 2 i_{1} - 3 i_{2} = 4 \to (1) \end{array}$

Consider ABHGEFA

$3 i_{2} - 2 + 5 (i_{1} + i_{2}) = 0 \Rightarrow 5 i_{1} + 8 i_{2} = 2 \to (2)$

Solving (1) & (2) we get

$i_{1} = \frac{28}{31} = 1 .23 A \Rightarrow i_{2} = 3 .55 A$

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