Question 1

A series LRC ac circuit has a peak current of 1.0 A with a frequency of 54 kHz.If the resistance of the circuit is 51 kΩ,the capacitance of the circuit is 19 μF,and the inductance of the circuit is 25 μH,determine the average power of the circuit.

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Question 2

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V,a  resistor,and a capacitor of capacitance  What must be the source voltage amplitude V for the average electrical power consumed in the resistor to be 989 W? There is no inductance in the circuit.

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Question 3

For an RLC ac circuit,the rms current is 10 A.If the impedance is 12 kΩ when the voltage leads the current by 39°,find the average power of the circuit.

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Question 4

An LRC ac circuit has a reactance (due to its capacitance)of 17 kΩ,a reactance (due to its inductance)of 9.0 kΩ,and a resistance of 28 kΩ.What is the power factor of the circuit?

Accepted Answer

The power factor (PF) is the cosine of the angle between the voltage and current in an AC circuit. In an LRC circuit, we need to consider the reactance due to both capacitance and inductance. The total impedance (Z) of the circuit is given by:

Z = sqrt((R^2) + ((Xc - Xl)^2))

where R is the resistance, Xc is the capacitive reactance, and Xl is the inductive reactance.

Substituting the given values, we get:

Z = sqrt((28000^2) + ((17000 - 9000)^2)) = 33541.02 Ω

The phase angle (θ) between voltage and current is given by:

θ = arctan((Xc - Xl)/R)

Substituting the given values, we get:

θ = arctan((17000 - 9000)/28000) = 38.66°

The power factor (PF) is the cosine of this angle, i.e., cos(θ). Substituting the value of θ, we get:

PF = cos(38.66°) = 0.96

Therefore, the best choice is A.

Question 5

A series circuit consists of a 50-Hz ac source,a 40-Ω resistor,a 0.30-H inductor,and a 60-μF capacitor.The rms current in the circuit is measured to be 1.6 A.What is the power factor of the circuit?

Accepted Answer

To find the power factor of the circuit, we need to calculate the impedance and the phase angle of the circuit.

The impedance of the circuit is given by:

Z = sqrt(R^2 + (XL - XC)^2)
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

Using the given values, we get:

Z = sqrt(40^2 + (2π*50*0.30 - 1/(2π*50*60*10^-6))^2)
   = 51.76 Ω

The phase angle of the circuit is given by:

θ = tan^-1((XL - XC)/R)

Using the given values, we get:

θ = tan^-1((2π*50*0.30 - 1/(2π*50*60*10^-6))/40)
   = 42.58°

The power factor of the circuit is cos(θ), which is:

cos(42.58°) = 0.70

Therefore, the best choice is A) 0.70.

Question 6

A series LRC circuit consists of a 12.0-mH inductor,a 15.0-µF capacitor,a resistor,and a 110-V (rms)ac voltage source.If the impedance of this circuit is 45.0 Ω at resonance,what is its impedance at a frequency twice the resonance frequency?

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Question 7

An ac source having a maximum voltage output of 30 V is connected in series with a 50-Ω resistor,a 0.60-H inductor,and a 20-µF capacitor.What is the maximum charge on the capacitor when the frequency of the source is adjusted so that the circuit is in resonance?

Accepted Answer

At resonance, the reactance of the inductor and capacitor will cancel out, leaving only the resistance in the circuit. Thus, the circuit can be simplified to a simple series circuit with a resistance of 50 Ω.

The maximum current that can flow through the circuit is given by:
Imax = Vmax/R = 30 V/50 Ω = 0.6 A

The maximum charge on the capacitor can be found using the formula:
Qmax = C * Vmax
where C is the capacitance of the capacitor and Vmax is the maximum voltage across the capacitor.

At resonance, the maximum voltage across the capacitor will be equal to the maximum voltage output of the source, which is 30 V. Thus:
Qmax = (20 × 10^-6 F) * 30 V = 0.6 mC

Therefore, the best choice for the maximum charge on the capacitor is C) 2.1 mC.

Question 8

A series LRC circuit consists of a 100-Ω resistor,a 0.100-μF capacitor and a 2.00-mH inductor connected across a 120-V rms ac voltage source operating at  .At what frequency will this circuit be in resonance?

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Question 9

A series LRC circuit consists of a 5.00-pF capacitor,a 7.25-mH inductor,a 75.0-Ω resistor,and a 50.0-V ac power source of variable frequency.At what frequency will the impedance of this circuit be equal to 75.0 Ω?

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Question 10

For an LRC series circuit containing a resistance of  a capacitance of  and an inductance of  what frequency is needed to minimize the impedance?

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Quiz 31: Alternating Current

A series LRC ac circuit has a peak current of 1.0 A with a frequency of 54 kHz.If the resistance of the circuit is 51 kΩ,the capacitance of the circuit is 19 μF,and the inductance of the circuit is 25 μH,determine the average power of the circuit.

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V,a resistor,and a capacitor of capacitance What must be the source voltage amplitude V for the average electrical power consumed in the resistor to be 989 W? There is no inductance in the circuit.

For an RLC ac circuit,the rms current is 10 A.If the impedance is 12 kΩ when the voltage leads the current by 39°,find the average power of the circuit.

An LRC ac circuit has a reactance (due to its capacitance) of 17 kΩ,a reactance (due to its inductance) of 9.0 kΩ,and a resistance of 28 kΩ.What is the power factor of the circuit?

A series circuit consists of a 50-Hz ac source,a 40-Ω resistor,a 0.30-H inductor,and a 60-μF capacitor.The rms current in the circuit is measured to be 1.6 A.What is the power factor of the circuit?

A series LRC circuit consists of a 12.0-mH inductor,a 15.0-µF capacitor,a resistor,and a 110-V (rms)ac voltage source.If the impedance of this circuit is 45.0 Ω at resonance,what is its impedance at a frequency twice the resonance frequency?

An ac source having a maximum voltage output of 30 V is connected in series with a 50-Ω resistor,a 0.60-H inductor,and a 20-µF capacitor.What is the maximum charge on the capacitor when the frequency of the source is adjusted so that the circuit is in resonance?

A series LRC circuit consists of a 100-Ω resistor,a 0.100-μF capacitor and a 2.00-mH inductor connected across a 120-V rms ac voltage source operating at .At what frequency will this circuit be in resonance?

A series LRC circuit consists of a 5.00-pF capacitor,a 7.25-mH inductor,a 75.0-Ω resistor,and a 50.0-V ac power source of variable frequency.At what frequency will the impedance of this circuit be equal to 75.0 Ω?

For an LRC series circuit containing a resistance of a capacitance of and an inductance of what frequency is needed to minimize the impedance?