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?

  • A 4 . 2 × 1 0 F
  • B 2 . 7 × 1 0 F
  • C 1 . 7 × 1 0 F
  • D 4 . 2 × 1 0 F
  • E 8 . 5 × 1 0 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 ?

  • A 𝑋 = 1 2 𝜋 𝑓 𝐶
  • B 𝑋 = 2 𝜋 𝐶 𝑓
  • C 𝑋 = 2 𝜋 𝑓 𝐶
  • D 𝑋 = 2 𝜋 𝑓 𝐶
  • E 𝑋 = 𝐶 2 𝜋 𝑓

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 ?

  • A 𝑍 = 𝑅 + ( 𝑋 𝑋 )
  • B 𝑍 = 𝑅 + 𝑋 + 𝑋
  • C 𝑍 = 𝑅 + ( 𝑋 + 𝑋 )
  • D 𝑍 = 𝑅 + 𝑋 𝑋
  • E 𝑍 = 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.

  • A 2.7 A
  • B 7.5 A
  • C 3.8 A
  • D 2.3 A
  • E 3.8 A

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

  • A 7.5 A
  • B 1.7 A
  • C 2.7 A
  • D 2.3 A
  • E 3.8 A

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