Electromagnetic Induction Chapter-Wise Test 21

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A solenoid with mutual inductance 0.2 H has a current change of 5 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.2 \times 5 = 1 \, \text{V} \).

0.5 V
1 V
1.5 V
2 V
2

A coil with \( L = 0.6 \, \text{H} \) has its current increased from 0 to 5 A in 0.5 s. What is the energy stored?

\( W = \frac{1}{2} L I^2 = \frac{1}{2} \times 0.6 \times (5)^2 = 0.3 \times 25 = 7.5 \, \text{J} \).

7 J
7.2 J
7.4 J
7.5 J
4

A magnet is moved towards a coil, inducing a current. If the magnet’s speed increases, what happens to the induced current?

Faster motion increases the rate of flux change, resulting in a larger induced emf and, assuming constant resistance, a larger induced current.

Increases
Decreases
Remains unchanged
Becomes zero
1

A magnet is dropped through a vertical copper tube. The magnet’s fall is slower than expected due to what effect?

The falling magnet induces currents in the copper tube, which create a magnetic field opposing the magnet’s motion, slowing its fall. This is an application of Lenz’s law.

Gravitational pull
Opposing magnetic field due to induced currents
Frictional force within the tube
Electrostatic repulsion
2

A coil of 130 turns and area 0.08 m² is in a 0.12 T field that drops to zero in 0.4 s. What is the induced emf?

\( \Delta \Phi = B A = 0.12 \times 0.08 = 0.0096 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 130 \times \frac{0.0096}{0.4} = 130 \times 0.024 = 3.12 \, \text{V} \).

2.8 V
3.0 V
3.12 V
3.5 V
3

A circular loop of radius 10 cm is deformed into a straight wire in a 0.1 T field. If the flux change occurs in 0.2 s, what is the induced emf?

Initial flux: \( \Phi = B A = 0.1 \times \pi \times (0.1)^2 = 0.00314 \, \text{Wb} \).

Final flux = 0.

\( \varepsilon = \frac{\Delta \Phi}{\Delta t} = \frac{0.00314}{0.2} = 0.0157 \, \text{V} \approx 0.016 \, \text{V} \).

0.01 V
0.016 V
0.02 V
0.025 V
2

A coil is wound tightly around a core material. If the current through it changes rapidly, the induced emf opposing this change is an example of which phenomenon?

This is self-induction, where a changing current in a coil induces an emf that opposes the change, proportional to the coil’s self-inductance.

Self-induction
Mutual induction
Electrostatic induction
Magnetic saturation
1

A solenoid of 400 turns and length 0.5 m induces an emf of 0.8 V in a nearby coil when its current changes from 2 A to 4 A in 0.2 s. What is the mutual inductance?

\( \varepsilon = M \frac{\Delta I}{\Delta t} \).

\( \Delta I = 4 - 2 = 2 \, \text{A} \), \( \Delta t = 0.2 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{0.8}{\frac{2}{0.2}} = \frac{0.8}{10} = 0.08 \, \text{H} \).

0.08 H
0.1 H
0.12 H
0.14 H
1

A coil with \( L = 0.3 \, \text{H} \) has its current increased from 0 to 6 A in 0.6 s. What is the energy stored?

\( W = \frac{1}{2} L I^2 = \frac{1}{2} \times 0.3 \times (6)^2 = 0.15 \times 36 = 5.4 \, \text{J} \).

5 J
5.2 J
5.3 J
5.4 J
4

A circular coil of radius 8 cm and 150 turns rotates at 25 rad/s in a 0.06 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.08)^2 = 0.0201 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 150 \times 0.06 \times 0.0201 \times 25 = 4.5225 \, \text{V} \approx 4.52 \, \text{V} \).

4.52 V
5.0 V
5.5 V
6.0 V
1

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