Q: A generator coil with $$N$$ turns and area $$A$$ rotates in a uniform magnetic field $$B at $$angular speed $$\omega. $$What is the expression for the peak emf generated?

$$\xi_{\text{peak}} = NAB\omega$$

Q: Which of the following is a correct unit for mutual inductance $$M$$?

$$1\ \text{Henry} = 1\ \text{V} \cdot \text{s}/\text{A}$$

Question 1

Which of the following energy sources does NOT primarily use water to generate electricity in conventional power plants?

Accepted Answer

Wind

Question 2

A generator coil with $$N$$ turns and area $$A$$ rotates in a uniform magnetic field $$B at $$angular speed $$\omega. $$What is the expression for the peak emf generated?

Accepted Answer

$$\xi_{	ext{peak}} = NAB\omega$$

Question 3

If a generator is rotating at a frequency $$f$$, what is the relationship between the angular speed $$\omega$$ and $$f$$?

Accepted Answer

$$\omega = 2\pi f$$

Question 4

A generator coil has a width $$W$$ and rotates at frequency $$f. $$What is the tangential speed $$v_T of a $$point on the edge of the coil?

Accepted Answer

$$v_T = W\pi f$$

Question 5

Which law explains the presence of a back emf in an electric generator?

Accepted Answer

Lenz's Law

Question 6

A generator produces a back emf that nearly equals the applied voltage. According to Ohm's Law, what happens to the current $$I in $$the circuit?

Accepted Answer

The current $$I$$ becomes very small.

Question 7

Which of the following factors does NOT affect the mutual inductance $$M$$ between two coils?

Accepted Answer

The resistance of the connecting wires

Question 8

Given a primary coil with $$N_1$$ turns and a secondary coil with $$N_2$$ turns, which equation correctly relates the voltages in a transformer?

Accepted Answer

$$\dfrac{V_2$}{V_1$} = \dfrac{N_2$}{N_1$}$$

Question 9

If the current in a coil changes at a rate $$\dfrac{dI}{dt}$$, what is the self-induced emf $$\xi in $$the coil with inductance $$L$$?

Accepted Answer

$$\xi = -L \dfrac{dI}{dt}$$

Question 10

A step-up transformer has $$N_2$$ \u003e $$N_1. $$What happens to the output voltage and current compared to the input?

Accepted Answer

Output voltage increases, output current decreases.

Question 11

The energy stored in an inductor with inductance $$L$$ carrying current $$I is $$given by:

Accepted Answer

$$E = \dfrac{1}{2} L I^2$

Question 12

Which of the following best describes the difference between mutual inductance and self-inductance?

Accepted Answer

Mutual inductance involves two coils, self-inductance involves one coil.

Question 13

A transformer is used to step down the voltage from $$120\ 	ext{V} to$$ $$12\ 	ext{V}. If $$the primary coil has $$N_1 = 1000$ turns, how many turns should the secondary coil have?

Accepted Answer

$$N_2 = 100$

Question 14

Which of the following statements about energy storage in inductors and capacitors is correct?

Accepted Answer

Inductors store energy in the magnetic field, capacitors in the electric field.

Question 15

A coil with $$N$$ turns and area $$A is $$placed in a magnetic field $$B$$ perpendicular to the plane of the coil. If the field changes from $$B_1 to$$ $$B_2 in $$time $$\Delta t$$, what is the average induced emf?

Accepted Answer

$$\xi = -N A \dfrac{B_2$ - B_1$}{\Delta t}$$

Question 16

Which of the following is a correct unit for mutual inductance $$M$$?

Accepted Answer

$$1\ 	ext{Henry} = 1\ 	ext{V} \cdot 	ext{s}/	ext{A}$$

Question 17

A coil with inductance $$L$$ and current $$I is $$disconnected from a battery. What happens to the energy stored in the inductor?

Accepted Answer

It is released as the current decreases, often as heat or electromagnetic radiation.

Question 18

Which of the following best explains why transformers only work with alternating current (AC) and not direct current (DC)?

Accepted Answer

Transformers require a changing magnetic flux, which only AC provides.

Question 19

A power plant generator produces electricity at $$60\ 	ext{Hz}. $$What is the angular speed $$\omega of $$the generator?

Accepted Answer

$$\omega = 2\pi 	imes 60 = 120\pi\ 	ext{rad/s}$$

Chapter 28 Part I - Electric Generators, Inductance, and Transformers

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