Two conducting circular loops of radii \(R_1\)\(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\) the mutual inductance \(M\) between them will be directly proportional to:
1. \(\frac{R^2_1}{R_2}\)
2. \(\frac{R^2_2}{R_1}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)
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 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.
2.
3.
4.
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. \(20~\text{J}\)
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.
2.
3.
4.
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
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
In a coil of resistance \(10\) \(\Omega\), the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:
1. \(2\)
2. \(6\)
3. \(4\)
4. \(8\)
A wheel with \(20\) metallic spokes, each \(1\) m long, is rotated with a speed of \(120\) rpm in a plane perpendicular to a magnetic field of \(0.4~\text{G}\). The induced emf between the axle and rim of the wheel will be:
\((1~\text{G}=10^{-4}~\text{T})\)
1. \(2.51 \times10^{-4}\) V
2. \(2.51 \times10^{-5}\) V
3. \(4.0 \times10^{-5}\) V
4. \(2.51\) V
The magnetic flux linked with a coil (in Wb) is given by the equation \(\phi=5 t^2+3 t+60\). The magnitude of induced emf in the coil at \(t=4\) s will be:
1. \(33\) V
2. \(43\) V
3. \(108\) V
4. \(10\) V