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 1 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 . 5 0 𝜏
  • B 0 . 3 3 𝜏
  • C 0 . 6 7 𝜏
  • D 0 . 6 9 𝜏
  • E 0 . 8 1 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 = 2 5 0 m H .

Determine the resistance of the circuit if 𝐿 = 2 5 0 m H .

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 = 2 0 V, inductance 𝐿 = 4 . 0 m H , 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 × 1 0 s .

Determine the voltage across 𝐿 at 𝑡 = 4 . 0 × 1 0 s .

Determine the voltage across 𝑅 at 𝑡 = 4 . 0 × 1 0 s .

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 = 2 0 V , 𝑅 = 8 . 0 1 Ω , and 𝑅 = 2 . 0 2 Ω .

Find 𝐼 1 at the instant switch 𝑆 is first closed.

Find 𝐼 2 at the instant switch 𝑆 is first closed.

Find 𝐼 3 at the instant switch 𝑆 is first closed.

Find 𝐼 3 after the currents have reached steady-state values.

Find 𝐼 2 after the currents have reached steady-state values.

Find 𝐼 1 after the currents have reached steady-state values.

Q7:

For the circuit shown, 𝜀 = 6 0 V , 𝑅 = 5 . 0 1 Ω , 𝑅 = 2 . 0 2 Ω , and 𝑅 = 4 . 0 3 Ω . Find the current through the inductor after the currents have reached steady-state values.

Q8:

For the circuit shown, 𝜀 = 6 0 V , 𝑅 = 5 . 0 1 Ω , 𝑅 = 2 . 0 2 Ω , 𝑅 = 4 . 0 3 Ω , and 𝐿 = 4 . 0 H . Find the current through the inductor 3 . 0 × 1 0 5 s after the switch is reopened.

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

Q9:

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

Find the current through 𝑅 1 .

Find the current through 𝑅 2 .

Find the current through the battery at 𝑡 = 2 . 0 s .

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