Question 1

A circular coil of radius 10 cm and a separate square coil of side 20 cm are both rotated in a magnetic field of 1.5 T. If the circular coil is rotated at a frequency of 60 Hz, then at what frequency must the square coil be rotated in order for both coils to have the same maximum induced voltage?
A) 47 Hz
B) 60 Hz
C) 76 Hz
D) 30 Hz
E) 19 Hz

Accepted Answer

The maximum induced voltage in a coil rotating in a magnetic field is given by the formula $EMF = NBA\omega$, where $N$ is the number of turns (assumed to be the same for both coils for this comparison), $B$ is the magnetic field strength, $A$ is the area of the coil, and $\omega$ is the angular velocity in radians per second. The frequency $f$ is related to $\omega$ by $\omega = 2\pi f$.For the circular coil, the area $A_{circle} = \pi r^2 = \pi (0.1)^2 = 0.01\pi$ m$^2$.For the square coil, the area $A_{square} = side^2 = (0.2)^2 = 0.04$ m$^2$.To have the same maximum induced voltage, we set the expressions for EMF equal to each other, leading to the relationship between their areas and angular velocities (or frequencies).Given that the circular coil is rotated at 60 Hz, we find the frequency for the square coil by ensuring the product of the area and frequency (which is proportional to angular velocity) is the same for both coils.$\frac{A_{circle}}{A_{square}} = \frac{f_{square}}{f_{circle}}$$\frac{0.01\pi}{0.04} = \frac{f_{square}}{60}$Solving for $f_{square}$, we get:$f_{square} = 60 \times \frac{0.01\pi}{0.04} = 60 \times \frac{\pi}{4} \approx 47$ Hz.Therefore, the square coil must be rotated at approximately 47 Hz to have the same maximum induced voltage as the circular coil rotated at 60 Hz.

Question 2

The rms value of house voltage in much of Europe is 220 V. What is the maximum voltage?
A) 440 V
B) 310 V
C) 220 V
D) 160 V
E) 120 V

Accepted Answer

The maximum voltage in an AC circuit is equal to the peak voltage, which is equal to the square root of 2 times the rms voltage. Therefore, the maximum voltage is 310 V, which is option B.

Question 3

If you double the rms voltage in an AC circuit, the peak voltage
A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of  .
D) decreases by a factor of  .
E) does not change.

Accepted Answer

A

Question 4

A square coil with 12 turns and side 5 cm is rotated in a uniform magnetic field of 1.2 T at an angular frequency of 90 radians per second. What is the maximum voltage induced in the coil?
A) 10 V
B) 3.2 V
C) 0.51 V
D) 0.27 V
E) None of the above.

Accepted Answer

The answer of A square coil with 12 turns and...

Question 5

A circular coil with 20 turns and radius 5 cm is rotated in a uniform magnetic field of 3.2 T. If the maximum voltage induced in the coil is 5 V, calculate the number of rotations of the coil per minute.
A) 600 revs per minute
B) 15 revs per minute
C) 5 revs per minute
D) 95 revs per minute
E) 200 revs per minute

Accepted Answer

The induced EMF in a rotating coil is given by:

$E = NBA\omega\sin(\omega t)$

where N is the number of turns in the coil, B is the magnetic field, A is the area of the coil, and $\omega$ is the angular velocity of the coil.

The maximum EMF is given by:

$E_{max} = NBA\omega$

Rearranging this equation, we get:

$\omega = \frac{E_{max}}{NBA}$

Substituting the given values, we get:

$\omega = \frac{5}{20	imes\pi	imes(0.05)^2	imes3.2}$

Solving for $\omega$, we get:

$\omega \approx 95\: rad/s$

To convert this to rotations per minute, we multiply by $60/2\pi$, giving:

$	ext{Rotations per minute} = \frac{95	imes60}{2\pi} \approx 905$

Rounding off to the nearest integer gives us the answer of 95 revs per minute, which is option D.

Question 6

How much does the maximum EMF produced by a generator a rotating coil) change if the area of the coil is doubled and the angular frequency halved?
A) It is the same.
B) It is increased by a factor of 2.
C) It is increased by a factor of 8.
D) It is decreased by a factor of 4.
E) It is impossible to tell given the information provided.

Accepted Answer

The maximum EMF produced by a generator is proportional to the product of the area of the coil and the angular frequency. If the area is doubled and the angular frequency is halved, the product remains the same, so the maximum EMF does not change.

Question 7

If you were to plug a 1200-W heater and a 600-W toaster into a 110-V electrical outlet, what total rms current would these two appliances draw if the wiring is parallel?
A) 5.45 A
B) 10.9 A
C) 11.6 A
D) 16.4 A
E) 23.1 A

Accepted Answer

In a parallel circuit, the total current is the sum of the currents through each appliance. The current through each appliance can be found using the formula $I = \frac{P}{V}$, where $I$ is the current, $P$ is the power, and $V$ is the voltage. For the 1200-W heater, $I_{heater} = \frac{1200}{110} = 10.91 \, A$. For the 600-W toaster, $I_{toaster} = \frac{600}{110} = 5.45 \, A$. The total current is $10.91 \, A + 5.45 \, A = 16.36 \, A$, which rounds to $16.4 \, A$.

Question 8

A flat, rectangular coil measuring 0.10 m by 0.20 m and containing 50 turns of wire is rotating at a constant speed of 100π rad/s in a magnetic field of 0.20 T. The maximum EMF induced in this coil is approximately
A) 1.0 V.
B) 10 V.
C) 63 V.
D) 44 V.
E) 0.13 V.

Accepted Answer

The formula for the maximum EMF induced in a rotating coil in a magnetic field is given by:
EMF = NABωsin(ωt) 
where N = number of turns, A = area of the coil, B = magnetic field strength, ω = angular velocity, and t = time.

Substituting the given values, we get:
EMF = 50 x 0.10 x 0.20 x 0.20 x 100π x sin(100πt) 
EMF = 63.66 sin(100πt)

The maximum value of sin(100πt) is 1, so the maximum EMF induced is:
EMFmax = 63.66 x 1 = 63.66 V

Therefore, the best choice is (C) 63 V.

Question 9

How much does the maximum EMF produced by a generator a rotating coil) change if the period of rotation is doubled?
A) It is the same.
B) It is doubled.
C) It is quadrupled.
D) It is halved.
E) It is quartered.

Accepted Answer

The maximum EMF produced by a generator is proportional to the angular velocity. If the period of rotation is doubled, the angular velocity is halved, thus the maximum EMF is also halved.

Question 10

As the frequency in this simple AC circuit increases, the rms power dissipated by the resistor
A) increases.
B) does not change.
C) may increase or decrease depending on the magnitude of the original frequency.
D) may increase or decrease depending on the magnitude of the resistance.
E) decreases.

Accepted Answer

The answer of  As the frequency in this simple...

Question 11

If you double the peak voltage in an AC circuit, the rms voltage
A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of  .
D) decreases by a factor of  .
E) does not change.

Accepted Answer

The answer of If you double the peak voltage in...

Question 12

An AC generator supplies 22 rms volts to a 30-Ω resistor at 50 Hz. What is the maximum current in the resistor?
A) 3.3 mA
B) 21 mA
C) 0.52 A
D) 0.73 A
E) 1.0 A

Accepted Answer

The answer of An AC generator supplies 22 rms volts...

Question 13

An AC motor can be turned into an AC generator by
A) reversing the poles of the permanent magnets.
B) applying a reverse voltage to the terminals of the motor.
C) mechanically rotating the coils instead of applying a voltage to the coil.
D) replacing the magnet with an armature coil and vice versa.
E) applying a DC voltage instead of an AC voltage.

Accepted Answer

An AC motor can be turned into an AC generator by mechanically rotating the coils instead of applying a voltage to the coil. This is known as the principle of electromagnetic induction, where a changing magnetic field induces an electromotive force (EMF) in a conductor. As the coils are rotated, they cut through the magnetic field produced by the permanent magnets, which induces an alternating current (AC) in the coils. The AC can then be collected and used as electricity. Reversing the poles of the permanent magnets, applying a reverse voltage, replacing the magnet with an armature coil, or applying a DC voltage instead of an AC voltage will not turn an AC motor into an AC generator.

Question 14

A simple generator consists of a single rectangular loop of wire rotating between two magnetic pole faces as shown. Which curve in the graph correctly represents the EMF as a function of the angle between the normal to the plane of the coil and the direction of the magnetic field?
A) 1
B) 2
C) 3
D) 4
E) None of these is correct.

Accepted Answer

The answer of  A simple generator consists of a...

Question 15

How much does the maximum EMF produced by a generator a rotating coil) change if the area of the coil is quadrupled?
A) It is the same.
B) It is increased by a factor of 16.
C) It is increased by a factor of 8.
D) It is increased by a factor of 4.
E) It is impossible to tell given the information provided.

Accepted Answer

The maximum EMF produced by a generator is proportional to the area of the coil. If the area is quadrupled, the maximum EMF will also be quadrupled since EMF is directly proportional to area. Therefore, the answer is (D) increased by a factor of 4.

Question 16

How much does the maximum EMF produced by a generator a rotating coil) change if its magnetic field is halved?
A) It is the same.
B) It is increased by a factor of 16.
C) It is decreased by a factor of 2.
D) It is increased by a factor of 4.
E) It is impossible to tell given the information provided.

Accepted Answer

The maximum EMF produced by a generator is given by the formula Emax = NBAω, where N is the number of turns in the coil, B is the magnetic field, A is the area of the coil, and ω is the angular velocity of the generator. If the magnetic field is halved, then Emax will decrease by a factor of 2, since it is directly proportional to B. Therefore, the correct answer is (C) It is decreased by a factor of 2.

Question 17

A motor sometimes burns out when its load is suddenly increased because the resulting sudden decrease in its rotational frequency causes
A) an increased back EMF and an increased current flow.
B) a decreased back EMF and a decreased current flow.
C) a decreased back EMF and zero current flow.
D) an increased back EMF and a decreased current flow.
E) a decreased back EMF and an increased current flow.

Accepted Answer

When the load on a motor increases suddenly, the rotational speed decreases, leading to a decrease in back EMF. This results in an increased current flow, which can cause the motor to burn out.

Question 18

As the frequency in this simple AC circuit increases, the rms current through the resistor
A) increases.
B) does not change.
C) may increase or decrease depending on the magnitude of the original frequency.
D) may increase or decrease depending on the magnitude of the resistance.
E) decreases.

Accepted Answer

The answer of  As the frequency in this simple...

Question 19

How much does the maximum EMF produced by a generator a rotating coil) change if the number of turns of the coil is tripled?
A) It is the same.
B) It is tripled.
C) It is increased by a factor of 9.
D) It is reduced by one-third.
E) It is impossible to tell given the information provided.

Accepted Answer

The maximum EMF produced by a generator is directly proportional to the number of turns of the coil. If the number of turns is tripled, the maximum EMF will also be tripled (as long as the other factors such as magnetic field strength and rotation speed remain constant). Therefore, the correct option is B.

Question 20

A 200-turn coil rotates in a magnetic field of magnitude 0.25 T at a frequency of 60 Hz. The area of the coil is 5.0 cm². What is the maximum EMF in the coil? A) 1.5 V B) 4.5 V C) 9.0 V D) 9.4 V E) 24 V

Accepted Answer

The maximum EMF is given by the equation: EMF_max = 2πfNAB, where f is the frequency, N is the number of turns, A is the area, and B is the magnitude of the magnetic field. 
Substituting the given values, we get: EMF_max = 2π(60)(200)(5.0×10^-4)(0.25) = 9.42 V. 
Rounding off to two significant figures, we get: EMF_max ≈ 9.4 V. Therefore, the best choice is D.

Quiz 21: Alternating-Current Circuits

A circular coil of radius 10 cm and a separate square coil of side 20 cm are both rotated in a magnetic field of 1.5 T. If the circular coil is rotated at a frequency of 60 Hz, then at what frequency must the square coil be rotated in order for both coils to have the same maximum induced voltage?

The rms value of house voltage in much of Europe is 220 V. What is the maximum voltage?

If you double the rms voltage in an AC circuit, the peak voltage

A square coil with 12 turns and side 5 cm is rotated in a uniform magnetic field of 1.2 T at an angular frequency of 90 radians per second. What is the maximum voltage induced in the coil?

A circular coil with 20 turns and radius 5 cm is rotated in a uniform magnetic field of 3.2 T. If the maximum voltage induced in the coil is 5 V, calculate the number of rotations of the coil per minute.

How much does the maximum EMF produced by a generator a rotating coil) change if the area of the coil is doubled and the angular frequency halved?

If you were to plug a 1200-W heater and a 600-W toaster into a 110-V electrical outlet, what total rms current would these two appliances draw if the wiring is parallel?

A flat, rectangular coil measuring 0.10 m by 0.20 m and containing 50 turns of wire is rotating at a constant speed of 100π rad/s in a magnetic field of 0.20 T. The maximum EMF induced in this coil is approximately

How much does the maximum EMF produced by a generator a rotating coil) change if the period of rotation is doubled?

As the frequency in this simple AC circuit increases, the rms power dissipated by the resistor

If you double the peak voltage in an AC circuit, the rms voltage

An AC generator supplies 22 rms volts to a 30-Ω resistor at 50 Hz. What is the maximum current in the resistor?

An AC motor can be turned into an AC generator by

A simple generator consists of a single rectangular loop of wire rotating between two magnetic pole faces as shown. Which curve in the graph correctly represents the EMF as a function of the angle between the normal to the plane of the coil and the direction of the magnetic field?

How much does the maximum EMF produced by a generator a rotating coil) change if the area of the coil is quadrupled?

How much does the maximum EMF produced by a generator a rotating coil) change if its magnetic field is halved?

A motor sometimes burns out when its load is suddenly increased because the resulting sudden decrease in its rotational frequency causes

As the frequency in this simple AC circuit increases, the rms current through the resistor

How much does the maximum EMF produced by a generator a rotating coil) change if the number of turns of the coil is tripled?

A 200-turn coil rotates in a magnetic field of magnitude 0.25 T at a frequency of 60 Hz. The area of the coil is 5.0 cm2. What is the maximum EMF in the coil?

A 200-turn coil rotates in a magnetic field of magnitude 0.25 T at a frequency of 60 Hz. The area of the coil is 5.0 cm². What is the maximum EMF in the coil?