Two coils have a mutual inductance $0.005$ H. The current changes in the first coil according to equation $I=I_{0}\sin\omega t$ where $I_{0}=2$ A and $\omega=100\pi$ rad/s. The maximum value of emf in the second coil is:
1. $4\pi$ V
2. $3\pi$ V
3. $2\pi$ V
4. $\pi$ V

For an inductor coil, $L = 0.04 ~\text{H}$, the work done by a source to establish a current of $5~\text{A}$ in it is:
1.  $0.5~\text{J}$
2.  $1.00~\text{J}$
3.  $100~\text{J}$
4.  $20~\text{J}$

For a coil having $L=2~\text{mH},$ the current flow through it is $I=t^2e^{-t}.$ The time at which emf becomes zero is:
1. $2$ s
2. $1$ s
3. $4$ s
4. $3$ s

The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in a time $\Delta t$. Then the total quantity of electric charge $Q$ that passes any point in the circuit during the time $\Delta t$ is represented by:
1. $Q= \frac{\Delta \phi}{R}$
2. $Q= \frac{\Delta \phi}{\Delta t}$
3. $Q=R\cdot \frac{\Delta \phi}{\Delta t}$
4. $Q=\frac{1}{R}\cdot \frac{\Delta \phi}{\Delta t}$

As a result of a change in the magnetic flux linked to the closed-loop shown in the figure, an emf, $V$ volt is induced in the loop. The work done (joules) in taking a charge $Q$ coulomb once along the loop is: