An emf of $15 V$ is applied to a circuit containing $5 H$ inductance and $10 \Omega$ resistance. The ratio of currents at time $t=\infty$ and $t=1 s$ after closing the switch is:

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 $t=40\; ms$ is close to: (Take $e^{2}=7.389$)

An induction coil stores $32 \ J$ of magnetic energy and dissipates energy as heat at the rate of $320 \ W$ when a current of $4 \ A$ is passed through it. Find the time constant of the circuit when the coil is joined across a battery.

In the given circuit,the switch is in position $a$. For what value of $R$ will the circuit have a time constant of $10\,\mu s$ in $K\Omega$?

In an $L-R$ circuit,the current reaches $\frac{3}{4}$ of its maximum value in $4 \ s$. What is the time constant of the $L-R$ circuit?

$A$ blackbox $(BB)$ which may contain a combination of electrical circuit elements (resistor, capacitor or inductor) is connected with other external circuit elements as shown in figure $(A)$. After the switch $S$ is closed at time $t=0$, the current $I$ as a function of time $t$ is shown in figure $(B)$. From this, we can infer that the blackbox contains: