# Worksheet: Circuits with Inductors and Capacitors in Series

In this worksheet, we will practice calculating the properties of circuits that contain inductors and capacitors in series.

Q1:

An circuit in an AM tuner (in a car stereo) uses a coil with an inductance of 2.5 mH and a variable capacitor. If the natural frequency of the circuit is to be adjustable over the range 540 to 1,600 kHz (the AM broadcast band), what range of capacitance is required?

• A F to F
• B F to F
• C F to F
• D F to F
• E F to F

Q2:

The self-inductance of an circuit is 0.20 mH. The circuit’s capacitance is 5.0 pF. What is the angular frequency of the current in the circuit?

Q3:

In an oscillating circuit, the maximum charge on the capacitor is C and the maximum current through the inductor is 8.0 mA.

What is the period of the oscillations?

• A s
• B s
• C s
• D s
• E s

How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged?

• A s
• B s
• C s
• D s
• E s

Q4:

When a camera uses a flash, a fully charged capacitor discharges through an inductor. In what time must the 0.200 amperes current through a 5.00 mH inductor be switched on or off to induce a 700 V emf?

Q5:

What is the self-inductance of an LC circuit that oscillates at 90 Hz when the capacitance is 30 µF?

Q6:

The self-inductance and capacitance of an oscillating LC circuit are L = 50 mH and C = 4.0 µF respectively.

What is the frequency of the oscillations?

If the maximum potential difference between the plates of the capacitor is 60 V, what is the maximum current in the circuit?

Q7:

In the circuit shown, S1 is opened and S2 is closed simultaneously, resulting in a circuit that consists of just an inductor and a capacitor. Determine the frequency of the resulting oscillations.

Determine the maximum charge on the capacitor.

Determine the maximum current through the inductor.

• A A
• B A
• C A
• D A
• E A

Determine the electromagnetic energy of the oscillating circuit.

Q8:

Part (a) of the diagram shows an circuit consisting of a resistor, an inductor, and a constant source of emf. and are switches. When is closed, the circuit is equivalent to the single-loop circuit shown in part (b) of the diagram. The value of the emf, , is equal to 18 V; the self-inductance, , of the inductor is 30 mH; and the resistor has a resistance of 8.0 Ω. Determine the inductive time constant of the circuit.

• A s
• B s
• C s
• D s
• E s

Determine the initial current through the resistor.

Determine the final current through the inductor.

Determine the current through the resistor when .

Determine the voltage across the inductor when .