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

Initially plane of a coil is parallel to the uniform magnetic field B. If in time ∆t the coil is perpendicular to the magnetic field, then charge flows in ∆t depends on this time as:

1. $\propto$ $∆t$

2. $\propto$ $\frac{1}{∆t}$

3. $\propto$ ${(∆t)}^0$

4. $\propto$ ${(∆t)}^2$

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\(L=2~\mathrm{mh},\) 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 $∆\varphi$ in a time ∆t. Then the total quantity of electric charge Q that passes any point in the circuit during the time ∆t is represented by:

1. $\mathrm{Q}=\frac{\mathrm{\Delta }\varphi }{\mathrm{R}}$

2. $\mathrm{Q}=\frac{\mathrm{\Delta }\varphi }{\mathrm{\Delta t}}$

3. $\mathrm{Q}=\mathrm{R}\cdot \frac{\mathrm{\Delta }\varphi }{\mathrm{\Delta t}}$

4. $\mathrm{Q}=\frac{1}{\mathrm{R}}\cdot \frac{\mathrm{\Delta }\varphi }{\mathrm{\Delta t}}$

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

1. QV

2. QV/2

3. 2QV

4. zero