Question 1

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 2

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 is suddenly increased, its rotational frequency decreases, leading to a decrease in back EMF. This decrease in back EMF allows more current to flow through the motor, potentially causing it to burn out if the current exceeds the motor's design limits.

Question 3

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

When a mechanical force is applied to an AC motor (such as rotating the coils), it causes the motor to produce an alternating electrical current. This is the basic principle behind how generators work. Reversing the polarity of the magnets (A) or applying a reverse voltage (B) would not convert the motor into a generator. Replacing the magnet with an armature coil (D) would not work because the magnet is a necessary component for generating an electrical current. Applying a DC voltage (E) would not work because a DC voltage only produces a unidirectional electrical current, whereas a generator needs to produce an alternating current.

Question 4

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 can be found by multiplying the rms value by the square root of 2 (1.414). Thus, the maximum voltage is 220 V x 1.414 = 310 V. Therefore, the best choice is B.

Question 5

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 answer of How much does the maximum EMF produced...

Question 6

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 7

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 8

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 in the coil is given by:
$EMF = 2\pi f N A B_{max}$,
where $N$ is the number of turns, $A$ is the area of the coil, and $B_{max}$ is the maximum magnitude of the magnetic field. Plugging in the given values, we get:
$EMF = 2\pi (60	ext{ Hz})(200)(5.0	ext{ cm}^2)(0.25	ext{ T}) = 9.42$ V
Therefore, the closest option is D) 9.4V.

Question 9

The resistance of the armature windings of DC motor is 5 $\Omega$. The motor is connected to a 120 V line. When the motor is spinning at full speed, it draws a current of 4 A. The bACk EMF at full speed is
A) 20 V
B) 100 V
C) 120 V
D) 40 V
E) 80 V

Accepted Answer

At full speed, the voltage across the armature windings can be calculated using Ohm's law:

V = IR + E

where V is the applied voltage (120V), I is the current through the windings (4A), R is the resistance of the windings (5Ω), and E is the back EMF.

Solving for E, we get:

E = V - IR
E = 120V - (4A * 5Ω)
E = 100V

Therefore, the back EMF at full speed is 100V, which is choice (B).

Question 10

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 two
C) it is increased by a factor of eight
D) it is decreased by a factor of four
E) it is impossible to tell given the information provided

Accepted Answer

The maximum EMF ($E_{max}$) produced by a generator is given by the formula $E_{max} = NBA\omega$, where $N$ is the number of turns in the coil, $B$ is the magnetic field strength, $A$ is the area of the coil, and $\omega$ is the angular frequency. If the area $A$ is doubled and the angular frequency $\omega$ is halved, the changes cancel each other out ($2A \times \frac{1}{2}\omega = A\omega$), leaving the maximum EMF unchanged.

Question 11

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 $\epsilon$ 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 12

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 13

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 100 $\pi$ 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 maximum EMF induced in the coil can be found using the formula: $EMF=NAB\omega_{max}$, where $N$ is the number of turns, $A$ is the area of the coil, $B$ is the magnetic field, and $\omega_{max}$ is the maximum angular velocity. Substituting in the given values, we get:

$EMF=50	imes 0.10	imes 0.20	imes 0.20	imes 100\pi= \boxed{63}$ V.

Question 14

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 nine
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. Therefore, if the number of turns is tripled, the maximum EMF will also triple.

Question 15

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 16

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 sixteen
C) it is increased by a factor of eight.
D) it is increased by a factor of four
E) it is impossible to tell given the information provided

Accepted Answer

The maximum EMF produced by a generator is directly proportional to the area of the coil. If the area of the coil is quadrupled, then the maximum EMF will also increase by a factor of four. Therefore, the correct answer is D, it is increased by a factor of four.

Question 17

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 sixteen
C) it is decreased by a factor of two
D) it is increased by a factor of four
E) it is impossible to tell given the information provided

Accepted Answer

The maximum EMF produced by a generator is given by the equation EMF = NABw where N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, and w is the angular velocity of the coil. If the magnetic field is halved, then the EMF will also be halved according to the equation. Therefore, the correct answer is C) it is decreased by a factor of two.

Question 18

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 19

An AC generator supplies 22 rms volts to a 30-$\Omega$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 20

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 answer of A circular coil with 20 turns and...

Quiz 9: Alternating-Current Circuits

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

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

An AC motor can be turned into an AC generator by

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

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

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?

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

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?

The resistance of the armature windings of DC motor is 5 $\Omega$ . The motor is connected to a 120 V line. When the motor is spinning at full speed, it draws a current of 4 A. The bACk EMF at full speed is

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 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 flat, rectangular coil measuring 0.10 m by 0.20 m and containing 50 turns of wire is rotating at a constant speed of 100 $\pi$ 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 number of turns of the coil is tripled?

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

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?

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?

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

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.