Question #118776

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

Calculate the values of the current through the circuit

Expert's answer

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

- 3V battery is being charged in this arrangement.

2) To find "i_2"

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

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