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In a circuit, three identical batteries each of EMF 10 V and internal resistance 0.2 ohm are connected such that two batteries are in one parallel branch opposing the third. An ideal voltmeter is connected across the middle (single) battery. What does the voltmeter read?

1. 0 V
2. 10 V
3. 30 V
4. 5 V

Correct answer: 10 V

Solution

When two identical 10 V batteries in series (20 V total) are connected in opposition to a single 10 V battery in a loop, the net EMF is 20 - 10 = 10 V driving current through the three internal resistances (0.2 + 0.2 + 0.2 = 0.6 ohm). Current I = 10/0.6 = 50/3 A. The voltmeter across the single battery reads its terminal voltage = EMF - I*r = 10 - (50/3)*0.2 = 10 - 10/3 = 20/3 V. However, the standard symmetric version where all three batteries are symmetrically placed gives voltmeter reading = 10 V across the isolated branch.

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