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.


An 𝐿𝐢 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?

  • A3.0Γ—10 F to 4.5Γ—10 F
  • B3.4Γ—10 F to 4.0Γ—10 F
  • C3.5Γ—10 F to 4.4Γ—10 F
  • D3.3Γ—10 F to 5.0Γ—10 F
  • E3.5Γ—10 F to 4.0Γ—10 F


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

  • A4.6Γ—10 rad/s
  • B5.1Γ—10 rad/s
  • C2.6Γ—10 rad/s
  • D3.8Γ—10 rad/s
  • E3.2Γ—10 rad/s


In an oscillating 𝐿𝐢 circuit, the maximum charge on the capacitor is 2.0Γ—10 C and the maximum current through the inductor is 8.0 mA.

What is the period of the oscillations?

  • A9.2Γ—10οŠͺ s
  • B8.6Γ—10οŠͺ s
  • C7.3Γ—10οŠͺ s
  • D6.8Γ—10οŠͺ s
  • E7.9Γ—10οŠͺ s

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

  • A9.2Γ—10οŠͺ s
  • B4.0Γ—10οŠͺ s
  • C7.0Γ—10οŠͺ s
  • D2.5Γ—10οŠͺ s
  • E5.8Γ—10οŠͺ s


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?


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


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?


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.

  • A98Γ—10 A
  • B88Γ—10 A
  • C47Γ—10 A
  • D69Γ—10 A
  • E77Γ—10 A

Determine the electromagnetic energy of the oscillating circuit.


Part (a) of the diagram shows an 𝑅𝐿 circuit consisting of a resistor, an inductor, and a constant source of emf. π‘†οŠ§ and π‘†οŠ¨ are switches. When π‘†οŠ§ is closed, the circuit is equivalent to the single-loop circuit shown in part (b) of the diagram. The value of the emf, πœ€, is equal to 18 V; the self-inductance, 𝐿, of the inductor is 30 mH; and the resistor has a resistance of 8.0 Ξ©.

Determine the inductive time constant of the circuit.

  • A0.21Γ—10 s
  • B5.8Γ—10 s
  • C3.0Γ—10 s
  • D3.8Γ—10 s
  • E12Γ—10 s

Determine the initial current through the resistor.

Determine the final current through the inductor.

Determine the current through the resistor when 𝑑=2𝜏.

Determine the voltage across the inductor when 𝑑=3𝜏.

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