Worksheet: Resonance in Alternating Current Circuits

In this worksheet, we will practice calculating the resonant frequency and Q value of simple resistive-capacitive-inductive circuits.

Q1:

A circuit consists of a resistor, a capacitor, and an inductor, all of which are in series. An alternating voltage source is connected to the circuit and an alternating current is generated. How does the resonant frequency of the circuit change if the resistance of the resistor is increased?

  • AThe resonant frequency does not change.
  • BThe resonant frequency increases.
  • CThe resonant frequency decreases.

Q2:

A circuit consists of a resistor, a capacitor, and an inductor, all of which are in series. An alternating voltage source is connected to the circuit and an alternating current is generated. How does the resonant frequency of the circuit change if the capacitance of the capacitor is increased?

  • AThe resonant frequency does not change.
  • BThe resonant frequency decreases.
  • CThe resonant frequency increases.

Q3:

Fill in the blank: In a series circuit containing a resistor, a capacitor, and an inductor, the resonant frequency of the circuit is the frequency of the circuit when its impedance has its value.

  • Aminimum
  • Bmean
  • Croot-mean-square
  • Dmaximum

Q4:

A circuit consists of a resistor, a capacitor, and an inductor, all of which are in series. An alternating voltage source is connected to the circuit and an alternating current is generated. How does the resonant frequency of the circuit change if the inductance of the inductor is increased?

  • AThe resonant frequency decreases.
  • BThe resonant frequency increases.
  • CThe resonant frequency does not change.

Q5:

What is the resonant frequency of the circuit shown in the diagram?

Q6:

What is the 𝑄 factor of a circuit that contains a 555 mH inductor and a 32.4 kΩ resistor if the frequency of the circuit is 247 kHz?

Q7:

A circuit containing a resistor, a capacitor, and an inductor is used as a receiver for electromagnetic waves with a frequency of 121 kHz. The resistance of the resistor is 116 kΩ. The circuit has a 𝑄 factor of 1.50. What is the capacitance of the capacitor in the circuit?

  • A1.50×10 F
  • B8.39×10 F
  • C7.56×10 F
  • D7.56×10 F
  • E4.75×10 F

Q8:

A circuit containing a capacitor and an inductor in series has a resonant frequency of 155 kHz. The capacitor in the circuit has a capacitance of 215 µF. What is the inductive reactance of the circuit?

  • A30.0 Ω
  • B4.90×10 Ω
  • C1.94 Ω
  • D4.78×10 Ω
  • E2.39×10 Ω

Q9:

A circuit containing a capacitor and an inductor in series has a resonant frequency of 575 kHz. The inductor in the circuit has an inductance of 1.25 H. What is the capacitance of the capacitor?

  • A6.13×10 F
  • B1.94×10 F
  • C2.42×10 F
  • D1.77×10 F
  • E9.90×10 F

Q10:

A circuit containing a resistor, a capacitor, and an inductor in series has a resonant frequency of 372 Hz. The resistor has a resistance of 440 Ω and the capacitor has a capacitance of 112 mF. The peak voltage across the circuit is 28 V. What is the peak current in the circuit when an alternating current in the circuit has a frequency of 372 Hz? Give your answer to two significant figures.

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