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

Engineering

Physics

AC Circuit Analysis

Question

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 = $\infty$ and at t = 40 s is close to : (Take e² = 7.389)

1.46

1.15

0.84

1.06

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$i = i_{0} (1 - e^{\frac{- t}{L / R}})$

$= 4 (1 - e^{\frac{- t}{0 .01 / 5}})$

= 4(1 – e^–500t)

$1_{\infty} = 4$

i₄₀ = 4(1 – e^–500 ^{× 40})

$= 4 (1 - \frac{1}{{(e^{2})}^{10000}}) = 4 (1 - \frac{1}{7 {.29}^{10000}})$

$\frac{i_{\infty}}{i_{40}} \approx 1$ slightly greater than one.