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In a series circuit the current varies as i(t) = 3 + 5t (i in amperes, t in seconds). With R = 4 ohm and L = 6 H, find the expression for the battery emf as a function of time.

1. (12 + 20t + 30) V = (42 + 20t) V
2. (12 + 20t) V
3. (30 + 20t) V
4. (42 - 20t) V

Correct answer: (12 + 20t + 30) V = (42 + 20t) V

Solution

For a series R-L circuit driven by a battery, emf = iR + L di/dt. Here iR = 4*(3 + 5t) = 12 + 20t, and L di/dt = 6*5 = 30. So emf = 12 + 20t + 30 = 42 + 20t volts.

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