Electromagnetic Induction Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In a setup with two coils, if the primary coil’s current is constant DC, what will be the induced emf in the secondary coil?

A constant DC current produces a steady magnetic field, resulting in no change in magnetic flux through the secondary coil, so the induced emf is zero.

Proportional to the current
Zero
Equal to the primary coil’s emf
Infinite
2

A circular coil of radius 6 cm and 200 turns rotates at 30 rad/s in a 0.08 T field. What is the maximum emf induced?

\( A = \pi r^2 = 3.14 \times (0.06)^2 = 0.0113 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 200 \times 0.08 \times 0.0113 \times 30 = 5.424 \, \text{V} \approx 5.42 \, \text{V} \).

5.42 V
5.6 V
5.8 V
6.0 V
1

A coil with \( L = 0.15 \, \text{H} \) has its current increased from 0 to 3 A in 0.3 s. What is the energy stored?

\( W = \frac{1}{2} L I^2 = \frac{1}{2} \times 0.15 \times (3)^2 = 0.075 \times 9 = 0.675 \, \text{J} \).

0.5 J
0.6 J
0.65 J
0.675 J
4

A solenoid with mutual inductance 0.35 H has a current change of 4 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.35 \times 4 = 1.4 \, \text{V} \).

1.0 V
1.2 V
1.4 V
1.6 V
3

A coil of self-inductance 0.7 H has its current increased from 2 A to 5 A in 0.3 s. What is the magnitude of the induced emf?

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

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

\( \varepsilon = 0.7 \times \frac{3}{0.3} = 0.7 \times 10 = 7 \, \text{V} \).

5 V
7 V
9 V
11 V
2

A circular loop is placed in a uniform magnetic field, and the field strength is increased steadily. What determines the magnitude of the induced emf in the loop?

According to Faraday’s law, the induced emf depends on the rate of change of magnetic flux, which increases with the rate at which the magnetic field strength changes.

Radius of the loop
Rate of change of magnetic field
Resistance of the loop
Temperature of the loop
2

A coil of self-inductance 0.9 H has its current increased from 1 A to 4 A in 0.25 s. What is the magnitude of the induced emf?

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

\( \Delta I = 4 - 1 = 3 \, \text{A} \), \( \Delta t = 0.25 \, \text{s} \).

\( \varepsilon = 0.9 \times \frac{3}{0.25} = 0.9 \times 12 = 10.8 \, \text{V} \).

9 V
10.8 V
12 V
14 V
2

A rectangular loop of sides 10 cm and 5 cm moves out of a 0.2 T magnetic field at 2 m/s perpendicular to the longer side. What is the motional emf induced?

For motional emf: \( \varepsilon = B l v \), where \( l \) is the length perpendicular to velocity.

Here, \( B = 0.2 \, \text{T} \), \( l = 0.05 \, \text{m} \), \( v = 2 \, \text{m/s} \).

\( \varepsilon = 0.2 \times 0.05 \times 2 = 0.02 \, \text{V} \).

0.01 V
0.02 V
0.04 V
0.06 V
2

A solenoid of 850 turns per meter and area 0.017 m² has a current drop from 10 A to 7 A in 0.25 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 \( l = 1 \, \text{m} \).

\( L = 4\pi \times 10^{-7} \times (850)^2 \times 0.017 \times 1 = 0.01541 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.01541 \times \frac{7 - 10}{0.25} = 0.01541 \times (-12) = 0.18492 \, \text{V} \approx 0.185 \, \text{V} \).

0.15 V
0.185 V
0.2 V
0.22 V
2

A conducting loop is expanded in a uniform magnetic field. The induced emf is caused by what physical process?

Expanding the loop increases the magnetic flux through it, and the rate of this flux change induces an emf as per Faraday’s law.

Change in magnetic flux through the loop
Change in resistance of the loop
Motion of charges due to thermal energy
Electrostatic charge separation
1

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