# 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 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 circuitβs capacitance is 5.0 pF. What is the angular frequency of the current in the circuit?

- A rad/s
- B rad/s
- C rad/s
- D rad/s
- E rad/s

**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 Β΅F?

**Q6: **

The self-inductance and capacitance of an oscillating LC circuit are L = 50 mH and C = 4.0 Β΅F 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, 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.