- 1(current)
Q. No.Two coils of conducting wire are wound closely around a solenoid, one above the other. If the number of turns of these coils are \(N_1\) and \(N_2,\) the mutual inductance between them is proportional to:
| 1. | \(N_1N_2\) | 2. | \(\Large\frac{N_1}{N_2}\) |
| 3. | \(\Large\frac{N_2}{N_1}\) | 4. | \(N_1^2N_2^2\) |
Subtopic: Â Mutual Inductance |
 74%
Level 2: 60%+
Hints
The mutual inductance between the two circuits can be determined by simply letting a current \(i\) flow through one circuit and finding the flux of the magnetic field through the second circuit: \(\phi_{2}=M_{12} i_{1}\), where \(M_{12}\) is the mutual inductance. Using this method, or otherwise determine the mutual inductance \((M)\) between a long straight wire, and a small coplanar loop of the area \(A\), located at a distance \(l\) from the wire. The value of \(M\) is:
| 1. | \( \dfrac{\mu_{0} l}{2 \pi}\) | 2. | \(\dfrac{\mu_{0} A}{2 \pi l}\) |
| 3. | \(\dfrac{\mu_{0} l^{3}}{4 \pi A}\) | 4. | \(\dfrac{\mu_{0} A^{2}}{2 \pi l^{3}}\) |
Subtopic: Â Mutual Inductance |
 80%
Level 1: 80%+
Hints
An inductor of inductance \(10~\text{mH}\) is connected in series with another identical inductor in series with each other. The inductance of the combined system is observed to be \(18~\text{mH}.\) The mutual inductance between the two inductors is:
| 1. | \(1~\text{mH}\) | 2. | \(2~\text{mH}\) |
| 3. | \(4~\text{mH}\) | 4. | \({\Large\frac{1}{2}}~\text{mH}\) |
Subtopic: Â Mutual Inductance |
 60%
Level 2: 60%+
Hints
A long solenoid of length \(L,\) having turns \(N \) and of radius of cross-section \(R\) has a single circular wire wound around it tightly, making a single turn. A current \(i=I_o\sin\omega t\) is passed through this outer wire. The peak EMF induced across the ends of the inner solenoid is (nearly), in magnitude:
| 1. | \(\dfrac{\pi \mu_{0} R^{2} N^{2} \omega I_{0}}{L}\) | 2. | \(\dfrac{\mu_{0} R^{2} \omega I_{0}}{N L}\) |
| 3. | \(\dfrac{\pi \mu_{0} L^{2} N \omega I_{0}}{R}\) | 4. | \(\dfrac{\pi \mu_{0} R^{2} N \omega I_{0}}{L}\) |
Subtopic: Â Mutual Inductance |
Level 3: 35%-60%
Hints
A small square loop (side: \(a\)) of conducting wire having a constant resistance \(\lambda\) per unit length, is placed at a very large distance \(r\) from an infinite, straight current-carrying wire, whose current is increasing at a constant rate: \(\dfrac{di}{dt}.\)
The mutual inductance between the square loop and the straight wire is proportional to:
The mutual inductance between the square loop and the straight wire is proportional to:
| 1. | \(\dfrac{a}{r}\) | 2. | \(\dfrac{a^2}{r}\) |
| 3. | \(\dfrac{a^2}{r^2}\) | 4. | \(\dfrac{a^4}{r^2}\) |
Subtopic: Â Mutual Inductance |
 62%
Level 2: 60%+
Hints
- 1(current)
Q. No.
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