A small square wire loop of side \(a\) is placed at the centre of a circular wire of radius \(r,\) both loops lying in the same plane. The mutual inductance between the two loops varies as:

1. \(\dfrac{r^2}{a^2}\) 2. \(\dfrac{a^2}{r}\)
3. \(a^2~r^2\) 4. \(\dfrac{a^2}{r^2}\)
Subtopic:  Mutual Inductance |
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Two coils \(1\) and \(2\), have mutual inductance \(M\) and resistance \(R\) each. A current flow in coil \(1\), which varies with time as; \(I_1=kt^{2},\) where \(k\) is constant, \(t\) is time. The total charge that flown through coil \(2\), between \(t=0\) to \(t=\dfrac{T}{2}\) will be:
1. \(\dfrac{MkT^2}{4R}\)

2. \(\dfrac{2MkT^2}{R}\)

3. \(\dfrac{MkT^2}{2R}\)

4.  Zero
Subtopic:  Mutual Inductance |
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Two coils are placed near each other, allowing a time-varying current in one coil to induce a time-varying current in the other. The mutual inductance between the coils depends on:

1. the rate of change of current in the two coils
2. the materials of the wires used in two coils
3. the currents in the two coils
4. the relative position and orientation of the two coils
Subtopic:  Mutual Inductance |
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In two circuits, \(1\) and \(2,\) where \({M}_{12}\)​ represents the mutual inductance of circuit \(1\) with respect to circuit \(2,\) and \({M}_{21}\)​ represents the mutual inductance of circuit \(2\) with respect to circuit \(1,\) while \(L_1\)​ and \(L_2\)​ denote the self-inductances of circuits \(1\) and \(2\) respectively, which of the following relations is correct?
1. \(M_{12}=M_{21}\)
2. \(M_{12}+M_{21}=0\)
3. \(M_{12}+M_{21}=L_{1}+L_{2}\)
4. \(\left|M_{12}+M_{21}\right|=\left|L_{1}-L_{2}\right|\)
Subtopic:  Mutual Inductance |
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