Worksheet: Circuits with Resistors and Inductors in Series

In this worksheet, we will practice calculating the voltage at a given time across a component in a circuit containing inductors and resistors in series.

Q1:

How long after switch 𝑆 is thrown does it take the current in the circuit shown to reach half its maximum value? Express your answer in terms of the time constant of the circuit.

  • A 0 . 8 1 𝜏
  • B 0 . 5 0 𝜏
  • C 0 . 3 3 𝜏
  • D 0 . 6 7 𝜏
  • E 0 . 6 9 𝜏

Q2:

The current in the RL circuit shown below reaches half its maximum value in 1.75 ms after the switch 𝑆 is thrown.

Determine the time constant of the circuit if 𝐿=250mH.

Determine the resistance of the circuit if 𝐿=250mH.

Q3:

The switch 𝑆 of the circuit shown is closed at 𝑡=0.

Determine the initial current through the battery.

Determine the steady-state current through the battery.

Q4:

For the circuit shown, emf 𝜀=20 V, inductance 𝐿=4.0mH, and resistance 𝑅=5.0 Ω. Steady state is reached with S closed and S open. S is then closed and immediately afterwards (at 𝑡=0) S is opened.

Determine the current through 𝐿 at 𝑡=0.

Determine the current through 𝐿 at 𝑡=4.0×10s.

Determine the voltage across 𝐿 at 𝑡=4.0×10s.

Determine the voltage across 𝑅 at 𝑡=4.0×10s.

Q5:

A resistor and a self-inductor are connected in series to a source of emf, creating an RL circuit. The current through the circuit increases to 20% of its steady-state value in 3.0 s. What is the time constant of the circuit?

Q6:

Consider the circuit shown with 𝜀=20V, 𝑅=8.0Ω, and 𝑅=2.0Ω.

Find 𝐼 at the instant switch 𝑆 is first closed.

Find 𝐼 at the instant switch 𝑆 is first closed.

Find 𝐼 at the instant switch 𝑆 is first closed.

Find 𝐼 after the currents have reached steady-state values.

Find 𝐼 after the currents have reached steady-state values.

Find 𝐼 after the currents have reached steady-state values.

Q7:

For the circuit shown, 𝜀=60V, 𝑅=5.0Ω, 𝑅=2.0Ω, and 𝑅=4.0Ω. Find the current through the inductor after the currents have reached steady-state values.

Q8:

For the circuit shown, 𝜀=60V, 𝑅=5.0Ω, 𝑅=2.0Ω, 𝑅=4.0Ω, and 𝐿=4.0H. Find the current through the inductor 3.0×10 s after the switch is reopened.

  • A 5 . 5 × 1 0 A
  • B 9 . 2 × 1 0 A
  • C 4 . 5 × 1 0 A
  • D 4 1 × 1 0 A
  • E 6 . 7 × 1 0 A

Q9:

The switch in the circuit shown is closed at 𝑡=0s.

Find the current through 𝑅.

Find the current through 𝑅.

Find the current through the battery at 𝑡=2.0s.

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