An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 Ω resistor. The ratio of the currents at time t = ∞ and at t = 40 s is close to: (Take e2 = 7.389) (a) 1.06 (b) 0.84 (c) 1.15 (d) 1.46

Answer: (a). i = i₀(1 - e-t/τ) with τ = L/R = 10×10⁻³5 = 2 ms Ratio (i∞)/(it) = 11 - e-t/τ At t = 40 s, t/τ = 2×10⁴, so e-t/τ ≈ 0 and the ratio is practically 1. The closest option is (a) 1.06.

An emf of 20 V is applied at time t = 0 to a circuit containing in… | JEE Main 2020 (7 Jan, Shift 2)

Q17JEE Main 2020 · 7 JAN · SHIFT 2Medium

Inductors & DC Transients (Mixed)

An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 $\Omega$ resistor. The ratio of the currents at time t = $\infty$ and at t = 40 s is close to: (Take e2 = 7.389)

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Answer: (a)

$i = i_0(1 - e^{-t/\tau})$ with $\tau = \frac{L}{R} = \frac{10\times10^{-3}}{5} = 2\text{ ms}$
Ratio $\frac{i_\infty}{i_t} = \frac{1}{1 - e^{-t/\tau}}$
At $t = 40\text{ s}$ , $t/\tau = 2\times10^4$ , so $e^{-t/\tau} \approx 0$ and the ratio is practically 1.
The closest option is (a) 1.06.

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