# 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

**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

**Q7: **

In the circuit shown, S_{1} is opened and S_{2} 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 Ξ©.

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 .