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In this lesson, we will learn how to calculate the voltage at a given time across a component in a circuit containing inductors and resistors in series.

Q1:

How long after switch π 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.

Q2:

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

Determine the time constant of the circuit if πΏ = 2 5 0 m H .

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

Q3:

The switch π of the circuit shown is closed at π‘ = 0 .

Determine the initial current through the battery.

Determine the steady-state current through the battery.

Q4:

For the circuit shown, emf π = 2 0 V, inductance πΏ = 4 . 0 m H , and resistance π = 5 . 0 Ξ©. Steady state is reached with S 1 closed and S 2 open. S 2 is then closed and immediately afterwards (at π‘ = 0 ) S 1 is opened.

Determine the current through πΏ at π‘ = 0 .

Determine the current through πΏ at π‘ = 4 . 0 Γ 1 0 β 4 s .

Determine the voltage across πΏ at π‘ = 4 . 0 Γ 1 0 β 4 s .

Determine the voltage across π at π‘ = 4 . 0 Γ 1 0 β 4 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 π = 2 0 V , π = 8 . 0 1 Ξ© , and π = 2 . 0 2 Ξ© .

Find πΌ 1 at the instant switch π is first closed.

Find πΌ 2 at the instant switch π is first closed.

Find πΌ 3 at the instant switch π is first closed.

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

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

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

Q7:

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

Q8:

For the circuit shown, π = 6 0 V , π = 5 . 0 1 Ξ© , π = 2 . 0 2 Ξ© , π = 4 . 0 3 Ξ© , and πΏ = 4 . 0 H . Find the current through the inductor 3 . 0 Γ 1 0 β 5 s after the switch is reopened.

Q9:

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

Find the current through π 1 .

Find the current through π 2 .

Find the current through the battery at π‘ = 2 . 0 s .

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