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What is the expression for the net charge generated in a circuit?

1. e = dφ/dt
2. i = e/R
3. ∫i dt = ∫(1/R) dφ
4. ∫i dt = (1/R) (φ₂ - φ₁)

Correct answer: ∫i dt = (1/R) (φ₂ - φ₁)

Solution

The total charge induced in a circuit is the time integral of current, and using Ohm's law (i = e/R) and Faraday's law (e = -dφ/dt), we can derive that the total charge is proportional to the change in magnetic flux divided by resistance, as given in option D.

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