Worksheet: Reactance of Alternating-Current Circuits

In this worksheet, we will practice calculating the capacitive reactance and inductive reactance of alternating-current RLC circuits.

Q1:

At what frequency is the reactance of a 20 Β΅F capacitor equal to that of a 10 mH inductor?

Q2:

A 100 mH inductor is connected across an emf that is given by 𝑣(𝑑)=(160)(120πœ‹π‘‘)Vsin. What is the reactance of the inductor? Answer to three significant figures.

Q3:

An inductor of 20.0 mH is connected across an ac source with a variable frequency and a constant-voltage amplitude of 9.0 V.

If the frequency of the ac source is fixed at 20 kHz, determine the reactance of the circuit.

  • A1.3Γ—10 Ξ©
  • B1.9Γ—10 Ξ©
  • C2.9Γ—10 Ξ©
  • D2.5Γ—10 Ξ©
  • E3.7Γ—10 Ξ©

If the frequency of the ac source is fixed at 20 kHz, determine the maximum current through the inductor.

  • A3.6Γ—10 A
  • B4.5Γ—10 A
  • C2.6Γ—10 A
  • D1.9Γ—10 A
  • E5.9Γ—10 A

If the frequency of the ac source is fixed at 60 Hz, determine the reactance of the circuit.

If the frequency of the ac source is fixed at 60 Hz, determine the maximum current through the inductor.

Q4:

An ac circuit contains an inductor and capacitor.

Find the reactance of a 2.0 mH inductor for a frequency of 60 Hz in the ac circuit.

Find the reactance of a 2.0 mH inductor for a frequency of 600 Hz in the ac circuit.

Find the reactance of a 20 mH inductor for a frequency of 6.0 Hz in the ac circuit.

Find the reactance of a 20 mH inductor for a frequency of 60 Hz in the ac circuit.

Find the reactance of a 2.0 mF capacitor for a frequency of 60 Hz in the ac circuit.

Find the reactance of a 2.0 mF capacitor for a frequency of 600 Hz in the ac circuit.

Q5:

What is the resistance 𝑅 in the circuit shown if the amplitude of the alternating current through the inductor is 4.24 A?

Q6:

A 5.0 mH inductor is connected in an ac circuit.

Calculate the reactance of the inductor for a current of frequency 60 Hz.

Calculate the reactance of the inductor for a current of frequency 600 Hz.

Calculate the reactance of the inductor for a current of frequency 6,000 Hz.

Q7:

A capacitor of 5.0 Β΅F is connected to an ac circuit.

Calculate the reactance of the capacitor for a current of frequency 60 Hz.

Calculate the reactance of the capacitor for a current of frequency 600 Hz.

Calculate the reactance of the capacitor for a current of frequency 6,000 Hz.

Q8:

A parallel plate capacitor has a plate area 𝐴=0.425m and plate separation of 0.0300 m. A time-varying potential difference is applied across the capacitor’s plates, modeled as 𝑉(𝑑)=𝑉(πœ”π‘‘)sin with 𝑉=80V. What angular frequency πœ” will induce a displacement current between the plates with a maximum value of 2.50 A?

  • A450Γ—10 rad/s
  • B250Γ—10 rad/s
  • C200Γ—10 rad/s
  • D300Γ—10 rad/s
  • E150Γ—10 rad/s

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