Q. No.Two concentric circular coils, one of small radius \({r_1}\) and the other of large radius \({r_2},\) such that \({r_1<<r_2},\) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is:
1. \(\dfrac{\mu_0\pi r_1^2}{3r_2}\)
2. \(\dfrac{2\mu_0\pi r_1^2}{r_2}\)
3. \(\dfrac{\mu_0\pi r_1^2}{r_2}\)
4. \(\dfrac{\mu_0\pi r_1^2}{2r_2}\)
The dimensions of mutual inductance \((M)\) are:
1. \(\left[M^2LT^{-2}A^{-2}\right]\)
2. \(\left[MLT^{-2}A^{2}\right]\)
3. \(\left[M^{2}L^{2}T^{-2}A^{2}\right]\)
4. \(\left[ML^{2}T^{-2}A^{-2}\right]\)
A pair of adjacent coils has a mutual inductance of \(1.5\) H. If the current in one coil changes from \(0\) to \(20\) A in \(0.5\) s, what is the change of flux linkage with the other coil?
| 1. | \(35\) Wb | 2. | \(25\) Wb |
| 3. | \(30\) Wb | 4. | \(20\) Wb |
| (a) | increases when they are brought nearer. |
| (b) | depends on the current passing through the coils. |
| (c) | increases when one of them is rotated about an axis. |
| (d) | is the same as \(M_{21}\) of coil \(2\) with respect to coil \(1\). |
1. (a), (d)
2. (a), (b), (c)
3. (b), (d)
4. (c), (d)
Read the passage given below and answer the given question.
Mutual Inductance is the phenomenon of induced emf in a coil, due to a change of current in the neighbouring coil. The amount of mutual inductance that links one coil to another depends very much on the relative positioning of the two coils, their geometry, and the relative separation between them. Mutual inductance between the two coils increases times if the coils are wound over an iron core of relative permeability \(\mu_r.\)
A short solenoid of radius \(a,\) number of turns per unit length \(n_1,\) and length \(L\) is kept coaxially inside a very long solenoid of radius \(b,\) number of turns per unit length \(n_2.\) What is the mutual inductance of the system?
| 1. | \(\mu_0 \pi b^2n_1n_2L\) | 2. | \(\mu_0 \pi a^2n_1n_2L^2\) |
| 3. | \(\mu_0 \pi a^2n_1n_2L\) | 4. | \(\mu_0 \pi b^2n_1n_2L^2\) |
1. \(\dfrac{2\sqrt{2}\mu _{0}L^{2}}{\pi l}\)
2. \(\dfrac{\mu_{0} \ell^{2}}{2 \sqrt{2} \pi \mathrm{L}} \)
3. \(\dfrac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi \mathrm{L}} \)
4. \(\dfrac{\mu_{0} L^{2}}{2 \sqrt{2} \pi \ell}\)
| 1. | current flowing in the two coils |
| 2. | material of the wires of the coils |
| 3. | the relative position and orientation of the two coils |
| 4. | rate of change in current in the two coils |
The smaller solenoid, which had a mutual inductance \(M_0\) with the larger one, is now rotated so that it makes an angle \(\theta\), with the larger one: the angle being measured between their axes. The mutual inductance is (nearly):
1. \(M_0\)
2. \(M_0\cos\theta\)
3. \(M_0\sin\theta\)
4. \(M_0\cos^2\theta\)
Two conducting circular loops of radii \(R_1\) and \(R_2\) 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. | \(\dfrac{R_1}{R_2}\) | 2. | \(\dfrac{R_2}{R_1}\) |
| 3. | \(\dfrac{R^2_1}{R_2}\) | 4. | \(\dfrac{R^2_2}{R_1}\) |
1. \(\dfrac{MkT^2}{4R}\)
2. \(\dfrac{2MkT^2}{R}\)
3. \(\dfrac{MkT^2}{2R}\)
4. zero
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