Electromagnetic Induction Chapter-Wise Test 7

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil is placed in a magnetic field that oscillates rapidly. The induced emf is higher when what property of the field increases?

The induced emf depends on the rate of change of magnetic flux (\( \varepsilon = -\frac{d\Phi}{dt} \)), which increases with the frequency of oscillation of the magnetic field.

Strength of the field
Frequency of oscillation
Direction of the field
Size of the coil
2

In an AC generator, increasing the number of turns in the coil affects what aspect of the output?

The emf (\( \varepsilon = N B A \omega \sin\omega t \)) is directly proportional to the number of turns, so more turns increase the amplitude of the induced emf.

Frequency
Amplitude of emf
Direction of current
Resistance of the coil
2

A wheel with 5 spokes of 0.65 m each rotates at 42 rpm in a 0.7 T field. What is the induced emf?

\( \omega = 2\pi \times \frac{42}{60} = 1.4\pi \, \text{rad/s} \).

\( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2} \times 0.7 \times 1.4\pi \times (0.65)^2 = 0.623 \, \text{V} \approx 0.62 \, \text{V} \).

0.5 V
0.55 V
0.6 V
0.62 V
4

A circular loop of radius 17 cm is deformed into a straight wire in a 0.15 T field in 0.5 s. What is the induced emf?

Initial flux: \( \Phi = B A = 0.15 \times \pi \times (0.17)^2 = 0.01363 \, \text{Wb} \).

Final flux = 0.

\( \varepsilon = \frac{\Delta \Phi}{\Delta t} = \frac{0.01363}{0.5} = 0.02726 \, \text{V} \approx 0.027 \, \text{V} \).

0.02 V
0.027 V
0.03 V
0.035 V
2

In an AC generator, the output voltage reverses direction every half-cycle due to what?

The coil’s rotation causes the flux to change sign every half-cycle as it passes from one field direction to the opposite, reversing the emf.

Change in field strength
Resistance variation
Capacitance effects
Reversal of flux change direction
4

A solenoid of 900 turns/m and area 0.018 m² has \( \mu_r = 1 \). What is its self-inductance? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

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

\( L = 1 \times 4\pi \times 10^{-7} \times (900)^2 \times 0.018 \times 1 = 0.01831 \, \text{H} \approx 0.018 \, \text{H} \).

0.015 H
0.016 H
0.018 H
0.02 H
3

A coil of 190 turns and area 0.03 m² is rotated at 40 Hz in a 0.09 T field. What is the maximum emf?

\( \omega = 2\pi v = 2\pi \times 40 = 80\pi \, \text{rad/s} \).

\( \varepsilon_0 = N B A \omega = 190 \times 0.09 \times 0.03 \times 80\pi = 128.91 \, \text{V} \approx 128.9 \, \text{V} \).

125 V
126 V
128 V
128.9 V
4

A rod rotates at 30 rad/s in a 0.6 T field. If the length from the axis to the tip is 0.8 m, what is the emf induced?

\( \varepsilon = \frac{1}{2} B \omega R^2 \).

\( \varepsilon = \frac{1}{2} \times 0.6 \times 30 \times (0.8)^2 = 5.76 \, \text{V} \).

5.0 V
5.5 V
5.76 V
6.0 V
3

A rod of length 0.35 m moves at 2.5 m/s in a 0.2 T field perpendicular to its length. What is the induced emf?

\( \varepsilon = B l v = 0.2 \times 0.35 \times 2.5 = 0.175 \, \text{V} \).

0.175 V
0.2 V
0.25 V
0.3 V
1

Two nearby coils are arranged such that a changing current in one induces an emf in the other. The strength of this effect is quantified by what property?

Mutual inductance measures the emf induced in one coil per unit rate of current change in the other, reflecting the strength of their magnetic coupling.

Mutual inductance
Self-inductance
Resistance
Capacitance
1

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