Question 1

A 104-Ω resistor is connected in series with a 14.7-µF capacitor and a 56-Hz,136-V (rms)line voltage.If electrical energy costs 4.8¢ per kWh,about how much does it cost to leave this circuit connected for 24 hours?
A)2¢
B)46¢
C)200¢
D)5¢

Accepted Answer

The answer of A 104-Ω resistor is connected in series...

Question 2

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 3

An electric motor produces 2.0 hp in a V_rms = 120 V circuit.Using 1 hp = 746 W,how long would it take this motor to do 1.0 kWh of work? A)0.67 min B)0.67 h C)1.3 min D)1.3 h

Accepted Answer

First, we need to convert the horsepower to watts:
2.0 hp * 746 W/hp = 1492 W

Then, we need to find the amount of time it takes to do 1.0 kWh of work:
1.0 kWh * 1000 W/kWh = 1000 W * h

We can use the formula W = P*t, where W is the work (in joules or watt-hours), P is the power (in watts), and t is the time (in hours). Rearranging the formula, we get:

t = W/P

Substituting the values we have:

t = (1000 W * h) / 1492 W
t = 0.67 h

Therefore, the answer is B) 0.67 h.

Question 4

A series RLC circuit is connected across a 240-Hz AC source,where ΔV_max = 140 V,R = 480 Ω,C = 0.250 μF,and L = 3.25 H.What is the average power delivered to this circuit? A)77.9 W B)1.78 W C)3.56 W D)0.890 W

Accepted Answer

The answer of ​A series RLC circuit is connected across...

Question 5

​A circuit consists of an AC audio amplifier,a resistor,and a speaker,all in series.The amplifier puts out an alternating voltage of 16.0 V (rms),the resistance of the resistor is 10.0 Ω,and the speaker has a resistance of 11.9 Ω.What is the time-averaged power delivered to the speaker?
A)​21.5 W
B)​30.5 W
C)​6.35 W
D)​8.69 W

Accepted Answer

The total resistance in the circuit is the sum of the resistor and the speaker, which is 21.9 Ω. The current in the circuit is given by I = V/R = 16.0 V / 21.9 Ω = 0.73 A (rms). The power delivered to the speaker is P = I²R = (0.73 A)² * 11.9 Ω = 6.35 W.

Question 6

What is the average power dissipation in an RLC series circuit in which R = 177 Ω,L = 0.060 H,and C = 8.65 µF driven at resonance by a 163-V (rms)source?
A)150 W
B)138 W
C)147 W
D)144 W
E)1 370 W

Accepted Answer

The average power dissipation in an RLC series circuit at resonance is given by:P = (Vrms^2) / Rwhere Vrms is the rms voltage of the source and R is the resistance of the circuit.In this case, Vrms = 163 V and R = 177 Ω, so:P = (163 V)^2 / 177 Ω = 147 WTherefore, the correct answer is C) 147 W.

Question 7

What is the average power dissipation in a series RC circuit if R = 6.35 kΩ,C = 2.64 µF,and V = (192 V)cos 115t?
A)2.29 W
B)5.81 W
C)2.90 W
D)3.23 W
E)6.47 W

Accepted Answer

The average power dissipation in a series RC circuit is given by $P = \frac{V_{rms}^2}{R}$, where $V_{rms}$ is the root mean square value of the voltage, and $R$ is the resistance. The given voltage is $V = (192 V)\cos 115t$, so the peak voltage $V_{peak}$ is 192 V. The $V_{rms}$ is $V_{peak}/\sqrt{2}$, which is $192/\sqrt{2}$ V. Plugging the values into the formula gives $P = \frac{(192/\sqrt{2})^2}{6350}$ (converting 6.35 kΩ to ohms), which calculates to approximately 2.29 W.

Question 8

An AM radio tuning circuit has a coil with an inductance of 3.93 mH and a capacitor set at 5.68 × 10−¹² F.What frequency will it detect? A)8.90E+5 Hz B)1.07E+6 Hz C)1.78E+6 Hz D)1.70E+5 Hz E)5.33E+5 Hz

Accepted Answer

The resonant frequency of a series RLC circuit, such as an AM radio tuning circuit, is given by the formula:

f = 1 / (2π√(LC))

Plugging in the values given, we get:

f = 1 / (2π√(3.93 mH × 5.68 × 10−11 F))

f = 1.07 × 106 Hz

Therefore, the circuit will detect a frequency of approximately 1.07 × 106 Hz, so the best choice is B.

Question 9

An AC series circuit contains a resistor of 30.0 Ω,a capacitor of 1.22 μF and an inductor of 154 mH.What frequency should be used to create a resonance condition in the circuit?
A)3.49E+2 Hz
B)8.48E+2 Hz
C)9.21E+2 Hz
D)3.67E+2 Hz
E)7.35E+2 Hz

Accepted Answer

The answer of An AC series circuit contains a resistor...

Question 10

A resistor,inductor and capacitor are connected in series,each with effective (rms)voltage of 80.0 V,160 V,and 84.0 V,respectively.If the resistor is rated at 15.0 Ω,what is the average power dissipated in the circuit?
A)812 W
B)427 W
C)309 W
D)589 W
E)559 W

Accepted Answer

The average power dissipated in a series RLC circuit is given by $P = \frac{V_{R}^2}{R}$, where $V_{R}$ is the voltage across the resistor and $R$ is the resistance. Given $V_{R} = 80.0 \, \text{V}$ and $R = 15.0 \, \Omega$, the power is $P = \frac{80.0^2}{15.0} = \frac{6400}{15.0} = 426.67 \, \text{W}$, which rounds to $427 \, \text{W}$.

Question 11

A series RLC AC circuit is at resonance.It contains a resistor of 18.7 Ω,a capacitor of 0.460 μF and an inductor of 70.9 mH.If an effective (rms)voltage of 41.0 V is applied,what is the effective (rms)current when the circuit is in resonance?
A)1.25 A
B)2.19 A
C)3.84 A
D)0.672 A
E)7.68 A

Accepted Answer

The answer of A series RLC AC circuit is at...

Question 12

An AC series circuit has 18.9-Ω resistance,21.1-Ω inductive reactance,and 15.5-Ω capacitive reactance.If an effective (rms)emf of 94 V is applied,what is the power output?
A)2.34E+2 W
B)1.60E+2 W
C)4.66E+2 W
D)4.30E+2 W
E)2.32E+2 W

Accepted Answer

First, we need to find the total impedance of the circuit using the formula: 
Z = √((R^2) + ((XL - XC)^2))
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. 
Plugging in the values, we get: 
Z = √((18.9^2) + ((21.1 - 15.5)^2)) = 12.78 Ω

Next, we can use the formula for power in an AC circuit: 
P = V^2/Z 
where V is the effective (rms) voltage. 
Plugging in the values, we get: 
P = (94^2)/12.78 = 690.93 W 
However, since this is an AC circuit, we need to consider the power factor (PF), which is the ratio of the true power (P) to apparent power (S). 
PF = P/S 
where S = V^2/Z 
Plugging in the values, we get: 
S = (94^2)/12.78 = 690.93 VA 
PF = 690.93/690.93 = 1 
Therefore, the power output is simply 690.93 W, or approximately 4.30E+2 W (in scientific notation). 
The answer is D.

Question 13

Find the resonant frequency for a series RLC circuit where R = 18.0 Ω,C = 9.7 µF,and L = 8.30 mH.
A)1.76E+3 Hz
B)5.61E+2 Hz
C)7.93E+2 Hz
D)1.98E+3 Hz
E)3.51E+2 Hz

Accepted Answer

The answer of Find the resonant frequency for a series...

Question 14

A series RLC circuit in a radio is in resonance with AM 700 kHz.If the radio station is changed to AM 2100 kHz,by what factor must the capacitance be multiplied to again achieve resonance?
A)​9
B)3
C)1
D)1/3
E)​1/9

Accepted Answer

The resonant frequency $f$ of an RLC circuit is given by $f = \frac{1}{2\pi\sqrt{LC}}$, where $L$ is the inductance and $C$ is the capacitance. To maintain resonance when the frequency is tripled (from 700 kHz to 2100 kHz), the product $LC$ must remain constant. Since $L$ is constant, $C$ must be adjusted inversely proportional to the square of the frequency change. Tripling the frequency ($\frac{2100}{700} = 3$) requires the capacitance to be divided by $3^2 = 9$, hence the factor is $1/9$.

Question 15

A resistor,inductor,and capacitor are connected in series,each with an effective (rms)voltage of 63 V,176 V,and 65 V,respectively.What is the magnitude of the phase angle in this circuit?
A)30°
B)64°
C)59°
D)60°
E)69°

Accepted Answer

The phase angle in an RLC series circuit is given by the arctan((V_L - V_C) / V_R). Substituting the given values: arctan((176V - 65V) / 63V) = arctan(111/63) ≈ 60°.

Question 16

A 58-Ω resistor,a 0.40-H inductor,and a 10.0-µF capacitor are connected in series to a 106-Hz source.The rms current in the circuit is 3.99 A.Find the rms voltage across the resistor,the inductor,and the capacitor.
A)231 V,1063 V,599 V (all rms)
B)231 V,1063 V,154 V (all rms)
C)599 V,169 V,154 V (all rms)
D)727 V,169 V,599 V (all rms)
E)727 V,1063 V,154 V (all rms)

Accepted Answer

The rms voltage across the resistor is 231 V, the rms voltage across the inductor is 1063 V, and the rms voltage across the capacitor is 154 V.

Question 17

In an LCR series circuit with X_L > X_C,the phase angle between the current and voltage phasors is 30°.If the AC frequency doubles,what is the magnitude of the resulting phase angle? A)30° B)less than 30° C)more than 30° D)Additional information is needed to reach a determination.

Accepted Answer

The answer of In an LCR series circuit with X_L...

Question 18

An electric motor produces 2.0 hp in a V_rms = 120 V circuit.What is I_rms for this motor? (1 hp = 746 W) A)12 A B)6.2 A C)0.62 A D)1.6 A

Accepted Answer

The power of an electric motor is given by P = VI, where P is the power in watts, V is the voltage in volts, and I is the current in amps. In this case, the power is 2.0 hp, which is equal to 1492 W, and the voltage is 120 V. Therefore, the current is I = P/V = 1492 W / 120 V = 12.4 A. The closest answer choice to this value is 12 A, so the correct answer is A.

Question 19

An FM radio tuning circuit has a coil with an inductance of 0.0036 mH.What is the value of the capacitance if the set is tuned to 91.3 MHz?
A)3.38E-12 F
B)2.65E-12 F
C)4.84E-13 F
D)8.45E-13 F
E)8.33E-12 F

Accepted Answer

The answer of An FM radio tuning circuit has a...

Question 20

An AC series circuit contains a resistor of 20.0 Ω,an inductor of 74.0 mH and a variable capacitor.If the frequency of the applied voltage is 423 Hz,to what setting should the capacitor be set if resonance is achieved?
A)1.89E-5 F
B)7.66E-6 F
C)5.09E-6 F
D)1.91E-6 F
E)1.91E-5 F

Accepted Answer

The answer of An AC series circuit contains a resistor...

Quiz 21: Alternating-Current Circuits and Electromagnetic Waves

A 104-Ω resistor is connected in series with a 14.7-µF capacitor and a 56-Hz,136-V (rms) line voltage.If electrical energy costs 4.8¢ per kWh,about how much does it cost to leave this circuit connected for 24 hours?

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

An electric motor produces 2.0 hp in a V_rms = 120 V circuit.Using 1 hp = 746 W,how long would it take this motor to do 1.0 kWh of work?

A series RLC circuit is connected across a 240-Hz AC source,where ΔV_max = 140 V,R = 480 Ω,C = 0.250 μF,and L = 3.25 H.What is the average power delivered to this circuit?

A circuit consists of an AC audio amplifier,a resistor,and a speaker,all in series.The amplifier puts out an alternating voltage of 16.0 V (rms) ,the resistance of the resistor is 10.0 Ω,and the speaker has a resistance of 11.9 Ω.What is the time-averaged power delivered to the speaker?

What is the average power dissipation in an RLC series circuit in which R = 177 Ω,L = 0.060 H,and C = 8.65 µF driven at resonance by a 163-V (rms) source?

What is the average power dissipation in a series RC circuit if R = 6.35 kΩ,C = 2.64 µF,and V = (192 V) cos 115t?

An AM radio tuning circuit has a coil with an inductance of 3.93 mH and a capacitor set at 5.68 × 10−¹² F.What frequency will it detect?

An AC series circuit contains a resistor of 30.0 Ω,a capacitor of 1.22 μF and an inductor of 154 mH.What frequency should be used to create a resonance condition in the circuit?

A resistor,inductor and capacitor are connected in series,each with effective (rms) voltage of 80.0 V,160 V,and 84.0 V,respectively.If the resistor is rated at 15.0 Ω,what is the average power dissipated in the circuit?

A series RLC AC circuit is at resonance.It contains a resistor of 18.7 Ω,a capacitor of 0.460 μF and an inductor of 70.9 mH.If an effective (rms) voltage of 41.0 V is applied,what is the effective (rms) current when the circuit is in resonance?

An AC series circuit has 18.9-Ω resistance,21.1-Ω inductive reactance,and 15.5-Ω capacitive reactance.If an effective (rms) emf of 94 V is applied,what is the power output?

Find the resonant frequency for a series RLC circuit where R = 18.0 Ω,C = 9.7 µF,and L = 8.30 mH.

A series RLC circuit in a radio is in resonance with AM 700 kHz.If the radio station is changed to AM 2100 kHz,by what factor must the capacitance be multiplied to again achieve resonance?

A resistor,inductor,and capacitor are connected in series,each with an effective (rms) voltage of 63 V,176 V,and 65 V,respectively.What is the magnitude of the phase angle in this circuit?

A 58-Ω resistor,a 0.40-H inductor,and a 10.0-µF capacitor are connected in series to a 106-Hz source.The rms current in the circuit is 3.99 A.Find the rms voltage across the resistor,the inductor,and the capacitor.

In an LCR series circuit with X_L > X_C,the phase angle between the current and voltage phasors is 30°.If the AC frequency doubles,what is the magnitude of the resulting phase angle?

An electric motor produces 2.0 hp in a V_rms = 120 V circuit.What is I_rms for this motor? (1 hp = 746 W)

An FM radio tuning circuit has a coil with an inductance of 0.0036 mH.What is the value of the capacitance if the set is tuned to 91.3 MHz?

An AC series circuit contains a resistor of 20.0 Ω,an inductor of 74.0 mH and a variable capacitor.If the frequency of the applied voltage is 423 Hz,to what setting should the capacitor be set if resonance is achieved?