Electromagnetic Induction Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil of self-inductance 0.6 H has its current decreased from 4 A to 1 A in 0.15 s. What is the magnitude of the induced emf?

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

\( \Delta I = 1 - 4 = -3 \, \text{A} \), \( \Delta t = 0.15 \, \text{s} \).

\( \varepsilon = 0.6 \times \frac{-3}{0.15} = 0.6 \times (-20) = -12 \, \text{V} \), magnitude = 12 V.

10 V
12 V
14 V
16 V
2

A solenoid of 450 turns and length 0.9 m induces an emf of 1.8 V in a nearby coil when its current changes from 2 A to 5 A in 0.3 s. What is the mutual inductance?

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

\( \Delta I = 5 - 2 = 3 \, \text{A} \), \( \Delta t = 0.3 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{1.8}{\frac{3}{0.3}} = \frac{1.8}{10} = 0.18 \, \text{H} \).

0.18 H
0.2 H
0.22 H
0.25 H
1

A circular coil of radius 10 cm and 220 turns rotates at 60 rad/s in a 0.02 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.1)^2 = 0.0314 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 220 \times 0.02 \times 0.0314 \times 60 = 8.2992 \, \text{V} \approx 8.3 \, \text{V} \).

8.3 V
8.5 V
9.0 V
9.5 V
1

A coil of 80 turns and area 0.05 m² is in a 0.1 T field that drops to zero in 0.25 s. What is the induced emf?

\( \Delta \Phi = B A = 0.1 \times 0.05 = 0.005 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 80 \times \frac{0.005}{0.25} = 80 \times 0.02 = 1.6 \, \text{V} \).

1.2 V
1.4 V
1.6 V
1.8 V
3

In a system of two coils, the mutual inductance depends on which property of the setup?

Mutual inductance depends on the geometry (e.g., coil sizes, separation, orientation) and the medium’s permeability, affecting how much flux from one coil links with the other.

Resistance of the coils
Current in the primary coil
Geometry and medium between the coils
Temperature of the coils
3

A coil of 180 turns and area 0.02 m² is rotated at 45 Hz in a 0.08 T field. What is the maximum emf?

\( \omega = 2\pi v = 2\pi \times 45 = 90\pi \, \text{rad/s} \).

\( \varepsilon_0 = N B A \omega = 180 \times 0.08 \times 0.02 \times 90\pi = 81.43 \, \text{V} \approx 81.4 \, \text{V} \).

78 V
79 V
80 V
81.4 V
4

In an AC generator, what happens to the induced emf when the rotational speed of the coil doubles?

The emf is proportional to the angular speed (\( \varepsilon = N B A \omega \)), so doubling the rotational speed doubles the emf.

Remains the same
Doubles
Halves
Quadruples
2

A metal ring is placed in a uniform magnetic field perpendicular to its plane. If the field strength decreases, the induced current in the ring flows in a direction to produce a magnetic field that does what?

According to Lenz’s law, the induced current opposes the decrease in magnetic flux by generating a magnetic field in the same direction as the original field.

Reinforces the original field
Opposes the original field
Cancels the field completely
Has no effect on the field
1

A solenoid of 800 turns per meter and area 0.013 m² has a current change from 9 A to 6 A in 0.2 s. What is the self-induced emf? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

\( L = \mu_0 n^2 A l \), assume \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (800)^2 \times 0.013 \times 1 = 0.01045 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.01045 \times \frac{6 - 9}{0.2} = 0.01045 \times (-15) = 0.15675 \, \text{V} \approx 0.157 \, \text{V} \).

0.12 V
0.157 V
0.18 V
0.2 V
2

A coil of 60 turns and area 0.04 m² is in a 0.1 T field that drops to zero in 0.2 s. What is the induced emf?

\( \Delta \Phi = B A = 0.1 \times 0.04 = 0.004 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 60 \times \frac{0.004}{0.2} = 60 \times 0.02 = 1.2 \, \text{V} \).

0.8 V
1.0 V
1.2 V
1.4 V
3

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