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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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