Worksheet: Impedance of Alternating Current Circuits

In this worksheet, we will practice calculating the impedance of simple resistive-capacitive-inductive circuits, using capacitive and inductive reactances.

Q1:

An alternating voltage source with a frequency of 50 Hz is connected to a 125 µF capacitor. What is the reactance of the capacitor? Give your answer to two significant figures.

Q2:

The reactance of the capacitor needed in an alternating current circuit is 120 Ω. The capacitor to be used has a 75 µF capacitance. What frequency must the alternating current have? Give your answer to two significant figures.

Q3:

An alternating voltage source with a frequency of 75 Hz is connected to a 35 mH inductor. What is the reactance of the circuit?

Q4:

What is the frequency of the alternating current in a circuit that contains a 0.25 H inductor that produces a reactance of 42 Ω?

Q5:

Which of the following graphs correctly shows how the reactance of a capacitor varies with the frequency of the alternating voltage source that the capacitor is connected to?

  • A
  • B
  • C
  • D

Q6:

What capacitance must a capacitor have to produce a 1.5 kΩ reactance in an alternating current circuit if the circuit has a frequency of 25 Hz?

  • A4.2×10 F
  • B4.2×10 F
  • C8.5×10 F
  • D2.7×10 F
  • E1.7×10 F

Q7:

Which of the following graphs correctly shows how the reactance of an inductor varies with the frequency of the alternating voltage source that the inductor is connected to?

  • A
  • B
  • C
  • D

Q8:

Which of the following formulas correctly relates the reactance 𝑋 of a capacitor to its capacitance 𝐶 when connected to an alternating voltage source with a frequency 𝑓?

  • A𝑋=2𝜋𝑓𝐶
  • B𝑋=2𝜋𝑓𝐶
  • C𝑋=12𝜋𝑓𝐶
  • D𝑋=𝐶2𝜋𝑓
  • E𝑋=2𝜋𝐶𝑓

Q9:

Which of the following formulas correctly relates the impedance 𝑍 of a circuit to the circuit’s capacitive reactance 𝑋, the circuit’s inductive reactance 𝑋, and the circuit’s resistance 𝑅?

  • A𝑍=𝑅+𝑋𝑋
  • B𝑍=𝑅+𝑋+𝑋
  • C𝑍=𝑅+(𝑋𝑋)
  • D𝑍=𝑅+𝑋𝑋
  • E𝑍=𝑅+(𝑋+𝑋)

Q10:

An alternating current circuit contains a resistor with a resistance of 25 Ω, an inductor with a 32 Ω inductive reactance, and a capacitor with a 12.8 Ω capacitive reactance. The peak voltage produced by the alternating voltage source powering the circuit is 120 V.

What is the peak current in the circuit? Give your answer to two significant figures.

  • A2.7 A
  • B2.3 A
  • C3.8 A
  • D5.8 A
  • E7.5 A

What is the root-mean-square current in the circuit? Give your answer to two significant figures.

  • A2.3 A
  • B2.7 A
  • C7.5 A
  • D1.7 A
  • E3.8 A

Q11:

An alternating current circuit contains a resistor with a resistance of 125 Ω, an inductor with a 450 Ω inductive reactance, and a capacitor with a 28.0 Ω capacitive reactance. What is the impedance of the circuit? Give your answer to three significant figures.

Q12:

An alternating voltage source with a frequency of 120 Hz is connected to an inductor, producing a reactance of 24 Ω. What is the inductance of the inductor? Give your answer to two significant figures.

Q13:

Which of the following formulas correctly relates the reactance 𝑋 of an inductor to its inductance 𝐿 when connected to an alternating voltage source with a frequency 𝑓?

  • A𝑋=2𝜋𝐿𝑓
  • B𝑋=𝐿2𝜋𝑓
  • C𝑋=2𝜋𝑓𝐿
  • D𝑋=12𝜋𝑓𝐿
  • E𝑋=2𝜋𝑓𝐿

Q14:

An alternating-current circuit has an impedance of 750 Ω. The circuit contains a resistor, an inductor with a 250 Ω inductive reactance, and a capacitor with a 45.0 Ω capacitive reactance. What is the resistance of the resistor? Give your answer to the nearest ohm.

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