# 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 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
• B
• C
• D
• E

Q2:

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

Determine the time constant of the circuit if .

Determine the resistance of the circuit if .

Q3:

The switch of the circuit shown is closed at .

Determine the initial current through the battery.

Determine the steady-state current through the battery.

Q4:

For the circuit shown, emf V, inductance , and resistance Ω. Steady state is reached with closed and open. is then closed and immediately afterwards (at ) is opened.

Determine the current through at .

Determine the current through at .

Determine the voltage across at .

Determine the voltage across at .

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 , , and .

Find at the instant switch is first closed.

Find at the instant switch is first closed.

Find at the instant switch is first closed.

Find after the currents have reached steady-state values.

Find after the currents have reached steady-state values.

Find after the currents have reached steady-state values.

Q7:

For the circuit shown, , , , and . Find the current through the inductor after the currents have reached steady-state values.

Q8:

For the circuit shown, , , , , and . Find the current through the inductor s after the switch is reopened.

• A A
• B A
• C A
• D A
• E A

Q9:

The switch in the circuit shown is closed at .

Find the current through .

Find the current through .

Find the current through the battery at .