Question 1

Consider an AC series circuit containing a coil,capacitor and resistance.Quadrupling the frequency will change the inductive reactance by what factor?
A) 1/4.0
B) 1.0
C) 2.0
D) 4.0
E) ​0.5

Accepted Answer

Inductive reactance (X_L) is directly proportional to the frequency (f), given by the formula X_L = 2πfL. Quadrupling the frequency will quadruple the inductive reactance.

Question 2

A resistor,inductor,and capacitor are connected in series,each with an effective (rms)voltage of 54 V,183 V,and 79 V,respectively.What is the magnitude of the phase angle in this circuit?
A) 27°
B) 68°
C) 60°
D) 63°
E) ​72°

Accepted Answer

The phase angle is given by the arctangent of the ratio of the inductive reactance to the capacitive reactance. In this case, the inductive reactance is 183 V / 54 V = 3.4 and the capacitive reactance is 79 V / 54 V = 1.46. Therefore, the phase angle is arctan(3.4 / 1.46) = 63°.

Question 3

An AC series circuit has 10.02-Ω resistance,19.78-Ω inductive reactance,and 7.40-Ω capacitive reactance.If an effective (rms)emf of 111 V is applied,what is the power output?
A) 620 W
B) 230 W
C) 1210 W
D) 490 W
E) ​590 W

Accepted Answer

The answer of An AC series circuit has 10.02-Ω resistance,19.78-Ω...

Question 4

A resistor,inductor,and capacitor are connected in series,each with effective (rms)voltage of 77 V,164 V,and 90 V,respectively.What is the value of the effective (rms)voltage of the applied source in the circuit?
A) 151 V
B) 107 V
C) 157 V
D) 331 V
E) ​202 V

Accepted Answer

The answer of A resistor,inductor,and capacitor are connected in series,each...

Question 5

In an AC circuit,the ratio of average current to maximum current is:
A) zero.
B) 0.5.
C) 0.707.
D) 1.0.

Accepted Answer

The answer of In an AC circuit,the ratio of average...

Question 6

An AC series circuit has 11.9 Ω resistance,15.57 Ω inductive reactance and 7.29 Ω capacitive reactance.If an effective (rms)emf of 103 V is applied,what is the effective (rms)current value?
A) 5.66 A
B) 7.10 A
C) 0.49 A
D) 17.5 A
E) ​5.10 A

Accepted Answer

The answer of An AC series circuit has 11.9 Ω...

Question 7

The power factor in an AC series circuit is equal to which of the following ratios?
A) resistance to inductive reactance
B) capacitive reactance to inductive reactance
C) inductive reactance to capacitive reactance
D) resistance to impedance

Accepted Answer

The power factor in an AC circuit is the ratio of the resistance to the total impedance of the circuit.

Question 8

In an RLC series circuit,if the AC frequency is increased to a very large value,what value does the phase angle between the current and voltage approach?
A) 90°
B) 0°
C) -90°
D) 45°

Accepted Answer

The answer of In an RLC series circuit,if the AC...

Question 9

A 48-Ω resistor,a 0.42-H inductor,and a 9.7-µF capacitor are connected in series to a 40-Hz source.The rms current in the circuit is 3.43 A.Find the rms voltage across the resistor,the inductor,and the capacitor.
A) 165 V,362 V,1407 V (all rms)
B) 165 V,362 V,236 V (all rms)
C) 1407V,58V,236V (all rms)
D) 517 V,58 V,1407 V (all rms)
E) ​517 V,362 V,236 V (all rms)

Accepted Answer

The correct answer is A because the rms voltage across the resistor is 165 V, the rms voltage across the inductor is 362 V, and the rms voltage across the capacitor is 1407 V.

Question 10

The power dissipated in an AC series circuit increases as the phase angle approaches what value?
A) zero
B) 45°
C) 90°
D) 180°

Accepted Answer

The power dissipated in an AC series circuit is maximum when the phase angle between the voltage and current is zero, indicating that the voltage and current are in phase, which corresponds to a purely resistive load where all the power is dissipated as useful work.

Question 11

In an RLC series circuit,if the AC frequency is decreased to a very small value,what value does the phase angle between the current and voltage approach?
A) 90°
B) 0°
C) -90°
D) 45°

Accepted Answer

When the AC frequency is decreased to a very small value, the circuit behaves as a purely resistive circuit and the phase angle between current and voltage approaches -90°. This is because the inductive reactance and capacitive reactance approach zero, leaving only the resistance to determine the phase angle. Therefore, option C (-90°) is the correct choice.

Question 12

A resistor and capacitor are connected in series with an applied AC voltage source.Separate voltmeter readings across the resistor and capacitor give values of 62 V and 93 V (rms),respectively.What is the effective (rms)voltage of the source?
A) 155 V
B) 145 V
C) 112 V
D) 79 V
E) ​158 V

Accepted Answer

When a resistor and capacitor are connected in series, the voltage drop across the resistor and capacitor must add up to the total voltage of the source. Let's call the voltage of the source V_s. Then we have:

V_s = V_R + V_C

where V_R is the voltage across the resistor and V_C is the voltage across the capacitor.

We are given that V_R = 62 V and V_C = 93 V. Therefore,

V_s = V_R + V_C = 62 V + 93 V = 155 V

This is the effective (rms) voltage of the source. Therefore, the correct choice is C.

Question 13

In an RLC series circuit the capacitive reactance is 43.6 Ω.If the AC frequency doubles,what will be the resulting capacitive reactance?
A) 30.8 Ω
B) 21.8 Ω
C) 61.7 Ω
D) 87.2 Ω
E) ​Additional information is need to find the value.

Accepted Answer

The capacitive reactance, XC = 1/(2πfC), where f is the frequency and C is the capacitance. 
If the frequency doubles, the new capacitive reactance will be XC' = 1/(2π(2f)C) 
Substituting XC = 43.6 Ω and solving for XC', we get XC' = 21.8 Ω. Therefore, the answer is B.

Question 14

A series circuit has equal values for resistance,capacitive reactance,and inductive reactance.The phase angle for this circuit is:
A) 60°.
B) -60°.
C) 180°.
D) not given.

Accepted Answer

The phase angle cannot be determined without knowing the specific values of resistance, capacitive reactance, and inductive reactance.

Question 15

A 103-Ω resistor is connected in series with a 13.9-µF capacitor and a 88-Hz,225-V (rms)line voltage.If electrical energy costs 3.1¢ per kWh,how much does it cost to leave this circuit connected for 20 hours?
A) 5.0¢
B) 117.4¢
C) 1.22¢
D) 11.7¢
E) ​12.2¢

Accepted Answer

The impedance of the circuit is calculated using the formula for series R-C circuits. The current is then found using Ohm's law. The power consumed is calculated using the formula P = I^2 * R. Finally, the energy cost is calculated by multiplying the power by the time and the cost per kWh.

Question 16

Consider an AC series circuit containing a coil,capacitor and resistance.Tripling the frequency will change the circuit's impedance by what factor?
A) 1/3
B) 1.0
C) 3
D) Information is insufficient to determine answer.

Accepted Answer

The impedance of an AC series circuit containing a coil, capacitor, and resistor depends on the frequency, but without specific values for the resistance, inductance, and capacitance, it's impossible to determine how tripling the frequency will affect the overall impedance.

Question 17

What is the average power dissipation in a series RC circuit if R = 2.12 kΩ,C = 2.25 µF,and V = (267 V)cos 479t?
A) 14.1 W
B) 33.6 W
C) 16.8 W
D) 20.0 W
E) ​39.9 W

Accepted Answer

The average power dissipation in a series RC circuit can be calculated using the formula P = Vrms^2 / R, where Vrms is the RMS voltage across the circuit.

First, we need to find the RMS voltage: 
Vrms = Vmax / sqrt(2) = 267 / sqrt(2) = 188.8 V

Then, we can plug in the values: 
P = Vrms^2 / R = (188.8)^2 / 2120 = 16.8 W

Therefore, the closest answer choice is A) 14.1 W.

Question 18

A resistor,inductor and capacitor are connected in series,each with effective (rms)voltage of 69 V,184 V and 58 V,respectively.If the resistor is rated at 31 Ω,what is the average power dissipated in the circuit?
A) 666 W
B) 154 W
C) 74 W
D) 320 W
E) ​584 W

Accepted Answer

The effective (rms) voltage across each element is given.
Let's calculate the effective (rms) current across each element.
For the resistor,
V = IR
69 = I(31)
I = 2.226 A (rms)

For the inductor,
V = IXL
184 = I(2πfL)
I = 18.4/(2πfL)

For the capacitor,
V = IXc
58 = I/(2πfC)
I = 58(2πfC)

Since the elements are in series, the same effective (rms) current flows through all of the elements.
Therefore, we can equate the currents to get:
2.226 = 18.4/(2πfL) = 58(2πfC)

Now we need to find the average power dissipated in the circuit:
P = I²R
P = (2.226)²(31)
P = 153.59 W

Therefore, the best choice is B) 154 W.

Question 19

Consider an AC series circuit containing a coil,capacitor and resistance.Tripling the frequency will change the capacitive reactance by what factor?
A) 1/3.0
B) 1.00
C) 1.7
D) 3.0
E) ​9.0

Accepted Answer

The capacitive reactance, XC, of a capacitor is given by:

XC = 1/(2πfC)

where f is the frequency and C is the capacitance.

When the frequency is tripled, the capacitive reactance becomes:

XC' = 1/(2π(3f)C)

XC' = (1/3) * (1/(2πfC))

So, the capacitive reactance is reduced by a factor of 1/3.0. Therefore, the correct answer is A) 1/3.0.

Question 20

In an RLC series circuit the phase angle between the current and voltages is 30°.If the AC frequency doubles,what is the resulting phase angle?
A) 30°
B) more than 30°
C) less than 30°
D) Additional information is needed to reach a determination.

Accepted Answer

Doubling the frequency increases the inductive reactance and decreases the capacitive reactance, which typically results in a larger phase angle in an RLC circuit.

Quiz 21: Alternating-Current Circuits and Electromagnetic Waves

Consider an AC series circuit containing a coil,capacitor and resistance.Quadrupling the frequency will change the inductive reactance by what factor?

A resistor,inductor,and capacitor are connected in series,each with an effective (rms) voltage of 54 V,183 V,and 79 V,respectively.What is the magnitude of the phase angle in this circuit?

An AC series circuit has 10.02-Ω resistance,19.78-Ω inductive reactance,and 7.40-Ω capacitive reactance.If an effective (rms) emf of 111 V is applied,what is the power output?

A resistor,inductor,and capacitor are connected in series,each with effective (rms) voltage of 77 V,164 V,and 90 V,respectively.What is the value of the effective (rms) voltage of the applied source in the circuit?

In an AC circuit,the ratio of average current to maximum current is:

An AC series circuit has 11.9 Ω resistance,15.57 Ω inductive reactance and 7.29 Ω capacitive reactance.If an effective (rms) emf of 103 V is applied,what is the effective (rms) current value?

The power factor in an AC series circuit is equal to which of the following ratios?

In an RLC series circuit,if the AC frequency is increased to a very large value,what value does the phase angle between the current and voltage approach?

A 48-Ω resistor,a 0.42-H inductor,and a 9.7-µF capacitor are connected in series to a 40-Hz source.The rms current in the circuit is 3.43 A.Find the rms voltage across the resistor,the inductor,and the capacitor.

The power dissipated in an AC series circuit increases as the phase angle approaches what value?

In an RLC series circuit,if the AC frequency is decreased to a very small value,what value does the phase angle between the current and voltage approach?

A resistor and capacitor are connected in series with an applied AC voltage source.Separate voltmeter readings across the resistor and capacitor give values of 62 V and 93 V (rms) ,respectively.What is the effective (rms) voltage of the source?

In an RLC series circuit the capacitive reactance is 43.6 Ω.If the AC frequency doubles,what will be the resulting capacitive reactance?

A series circuit has equal values for resistance,capacitive reactance,and inductive reactance.The phase angle for this circuit is:

A 103-Ω resistor is connected in series with a 13.9-µF capacitor and a 88-Hz,225-V (rms) line voltage.If electrical energy costs 3.1¢ per kWh,how much does it cost to leave this circuit connected for 20 hours?

Consider an AC series circuit containing a coil,capacitor and resistance.Tripling the frequency will change the circuit's impedance by what factor?

What is the average power dissipation in a series RC circuit if R = 2.12 kΩ,C = 2.25 µF,and V = (267 V) cos 479t?

A resistor,inductor and capacitor are connected in series,each with effective (rms) voltage of 69 V,184 V and 58 V,respectively.If the resistor is rated at 31 Ω,what is the average power dissipated in the circuit?

Consider an AC series circuit containing a coil,capacitor and resistance.Tripling the frequency will change the capacitive reactance by what factor?

In an RLC series circuit the phase angle between the current and voltages is 30°.If the AC frequency doubles,what is the resulting phase angle?