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An EMF of 15 V is applied to a circuit containing an inductance of 5 H and a resistance of 10 ohm in series. Find the ratio of the current at t = infinity to the current at t = 1 second.

1. 1/(1 - e⁻²)
2. 1 - e⁻²
3. 1/(1 - e⁻⁰.5)
4. e⁻²

Correct answer: 1/(1 - e⁻²)

Solution

I(t) = (EMF/R)(1 - e^(-Rt/L)). tau = L/R = 5/10 = 0.5 s. I(infinity) = EMF/R = 15/10 = 1.5 A. I(1 s) = 1.5*(1 - e^(-1/0.5)) = 1.5*(1 - e⁻²). Ratio I(infinity)/I(1) = 1/(1 - e⁻²) approx 1/(1-0.135) = 1.156.

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