Question

Two batteries P and Q each of Emf 8 V and 3 V have internal resistance of 2 Ω and 4 Ω respectively.
Calculate the values of the current through the circuit

Answer 1

Explanations & Calculations

• Two batteries (P & Q) could be connected in either way as show above.
• For the ease of understanding, it's allowed to represent the internal resistance of the battery, just outside it.
• And apply Kirchoff's voltage law in the shown direction.

1) To find $i_1$ ,

$\qquad\qquad \begin{aligned} \small 8V-i_1\times 2\Omega-i_1\times 4\Omega-3V &= \small 0\\ \small i_1 \times 6\Omega &= \small 5V\\ \small i_1 &= \small \bold{0.833A} \end{aligned}$

• 3V battery is being charged in this arrangement.

2) To find $i_2$

$\qquad\qquad \begin{aligned} \small 8V-i_2\times2\Omega -i_2 \times 4\Omega +3V &= \small 0\\ \small i_2 \times 6 \Omega &= \small 11V\\ \small i_2 &= \small \bold{1.833 A} \end{aligned}$