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A student connects one cell to a circuit and measures current I1. Adding a second identical cell in series gives current I2. Connecting the two identical cells in parallel instead gives current I3. Which relation among I1, I2, I3 is correct?

1. 3 I3 I2 = 2 I1 (I2 + I3)
2. I3 I2 = I1 (I2 + I3)
3. 2 I3 I2 = 3 I1 (I2 + I3)
4. 3 I3 I2 = I1 (I2 + I3)

Correct answer: 3 I3 I2 = 2 I1 (I2 + I3)

Solution

Writing the three currents and eliminating E, R, r leads to the relation 3 I2 I3 = 2 I1 (I2 + I3).

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