Question

An emf of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = ∞ and at t = 1 second is

• A. $\frac{e^{1/2}}{e^{1/2} - 1}$
• B. $\frac{e^{2}}{e^{2} - 1}$
• C. $1 - e^{- 1}$
• D. e^{– 1}

Answer 1

Answer: (B)

$\frac{e^{2}}{e^{2} - 1}$

Answer 2

By using $i = i_{0}\left( 1 - e^{- \frac{Rt}{L}} \right)$; At t = ∞, i = i₀ and at t = 1 sec $i = i_{0}\left( 1 - e^{- \frac{10 \times 1}{5}} \right)$;$i = i_{0}(1 - e^{- 2}) = i_{0}\left( \frac{e^{2} - 1}{e^{2}} \right)$;

$\frac{i_{0}}{i} = \frac{e^{2}}{e^{2} - 1}$