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 𝐿 𝐢 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 6 0 0 kHz (the AM broadcast band), what range of capacitance is required?

  • A 3 . 4 Γ— 1 0 βˆ’ 1 1 F to 4 . 0 Γ— 1 0 βˆ’ 1 1 F
  • B 3 . 0 Γ— 1 0 βˆ’ 1 1 F to 4 . 5 Γ— 1 0 βˆ’ 1 2 F
  • C 3 . 3 Γ— 1 0 βˆ’ 1 1 F to 5 . 0 Γ— 1 0 βˆ’ 1 2 F
  • D 3 . 5 Γ— 1 0 βˆ’ 1 1 F to 4 . 0 Γ— 1 0 βˆ’ 1 2 F
  • E 3 . 5 Γ— 1 0 βˆ’ 1 1 F to 4 . 4 Γ— 1 0 βˆ’ 1 2 F

Q2:

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

  • A 3 . 8 Γ— 1 0 βˆ’ 7 rad/s
  • B 2 . 6 Γ— 1 0 βˆ’ 7 rad/s
  • C 4 . 6 Γ— 1 0 βˆ’ 7 rad/s
  • D 3 . 2 Γ— 1 0 βˆ’ 7 rad/s
  • E 5 . 1 Γ— 1 0 βˆ’ 7 rad/s

Q3:

In an oscillating 𝐿 𝐢 circuit, the maximum charge on the capacitor is 2 . 0 Γ— 1 0 βˆ’ 6 C and the maximum current through the inductor is 8.0 mA.

What is the period of the oscillations?

  • A 8 . 6 Γ— 1 0 βˆ’ 4 s
  • B 9 . 2 Γ— 1 0 βˆ’ 4 s
  • C 7 . 3 Γ— 1 0 βˆ’ 4 s
  • D 7 . 9 Γ— 1 0 βˆ’ 4 s
  • E 6 . 8 Γ— 1 0 βˆ’ 4 s

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

  • A 4 . 0 Γ— 1 0 βˆ’ 4 s
  • B 5 . 8 Γ— 1 0 βˆ’ 4 s
  • C 7 . 0 Γ— 1 0 βˆ’ 4 s
  • D 9 . 2 Γ— 1 0 βˆ’ 4 s
  • E 2 . 5 Γ— 1 0 βˆ’ 4 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, 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 7 7 Γ— 1 0 βˆ’ 3 A
  • B 6 9 Γ— 1 0 βˆ’ 3 A
  • C 4 7 Γ— 1 0 βˆ’ 3 A
  • D 8 8 Γ— 1 0 βˆ’ 3 A
  • E 9 8 Γ— 1 0 βˆ’ 3 A

Determine the electromagnetic energy of the oscillating circuit.

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