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Self Induction

Practice Questions:

Question 1: easy

The self inductance of a toroid is :

1. \[\frac{\mu_{0}N^{2}r^{2}}{2R_{m}}\]

2. \[\frac{\mu_{0}N^{2}\pi r}{2R_{m}}\]

3. \[\frac{\mu_{0}N^{2}r}{2R_{m}}\]

4. \[\frac{\mu_{0}N^{2}r\pi}{2R_{m}}\]

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Question 2: moderate

A varying current in a coil changes from 10 amp to zero in 0.5 sec. If average EMF is induced in
the coil is 220 volts, the self inductance of coil is :

1. 5 H

2. 10 H

3. 11 H

4. 12 H

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Question 3: moderate

How much length of a very thin wire is required to obtain a solenoid of length l0 and inductance L.

1. \[\sqrt{\frac{2\pi Ll_{0}}{\mu_{0}}}\]

2. \[\sqrt{\frac{4\pi Ll_{0}}{\mu_{0}^{2}}}\]

3. \[\sqrt{\frac{4\pi Ll_{0}}{\mu_{0}}}\]

4. \[\sqrt{\frac{8\pi Ll_{0}}{\mu_{0}}}\]

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Question 4: difficult

What is the mutual inductance of a two-loop system as shown with centre separation l ?

1. \[\frac{\mu_{0}\pi a^{4}}{8l^{3}}\]

2. \[\frac{\mu_{0}\pi a^{4}}{4l^{3}}\]

3. \[\frac{\mu_{0}\pi a^{4}}{6l^{3}}\]

4. \[\frac{\mu_{0}\pi a^{4}}{2l^{3}}\]

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Question 5: easy

A coil resistance 20 Ω and inductance 5 H is connected with a 100 V battery. Energy stored in the coil will be :

1. 41.5 J

2. 62.50 J

3. 125 J

4. 250 J

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I = \frac{V}{R} = \frac{100}{20} = 5 \text{ A}

U = \frac{1}{2} L I^2 = \frac{1}{2} \times 5 \times 5^2 = 62.5 \text{ J}

Energy stored = 62.5 J

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Question 6: easy

A current of \(2\text{ A}\) is increasing at a rate of \(4\text{ A/s}\) through a coil of inductance \(2\text{ H}\). The energy stored in the inductor per unit time in given instant is:

1. \(2\text{ J/s}\)

2. \(1\text{ J/s}\)

3. \(16\text{ J/s}\)

4. \(4\text{ J/s}\)

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Formula for rate of change of energy in an inductor is \(\frac{dU}{dt} = LI\frac{dI}{dt}\). Given \(L = 2\text{ H}\), \(I = 2\text{ A}\), and \(\frac{dI}{dt} = 4\text{ A/s}\), we get \(\frac{dU}{dt} = 2 \times 2 \times 4 = 16\text{ J/s}\).

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Question 7: easy

A coil of \(\text{Cu}\) wire (radius \(r\), self inductance \(L\)) is bent in two concentric turns each having radius \(\frac{r}{2}\). The self-inductance now is:

1. \(2L\)

2. \(L\)

3. \(4L\)

4. \(\frac{L}{2}\)

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Self-inductance of a coil is \(L \propto N^2 r\). When bent into \(2\) turns of radius \(r/2\), new self-inductance is \(L' \propto (2)^2 (r/2) = 2 L\).

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Question 8: easy

Assertion (A): The self inductance of a solenoid can be increased by decreasing length if number of turns are fixed.

Reason (R): Self inductance of a solenoid is directly proportional to current passing through it.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

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Self inductance of a solenoid is given by \(L = \frac{\mu_0 N^2 A}{l}\). So, Assertion (A) is true as \(L\) is inversely proportional to \(l\). Self inductance \(L\) is a property of the coil's geometry and material, not dependent on current. So, Reason (R) is false. Thus, (A) is true but (R) is false.

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