Worksheet: Circuits with Resistors, Inductors, and Capacitors in Series

In this worksheet, we will practice describing the time evolution of circuits containing inductors, capacitors, and resistors.


An oscillating circuit has an inductance 𝐿=10 mH, a capacitance 𝐶=1.5 µF, and a resistance 𝑅=2.0 Ω. What is the time required for the amplitude of oscillations in this circuit to drop to half their initial value?


In an oscillating RLC circuit, 𝑅=6.00Ω, 𝐿=9.00mH, and 𝐶=650µF. What is the angular frequency of the oscillations?


What resistance must be connected in series with a 200 mH inductor and a 12 µF capacitor for the resulting RLC oscillating circuit’s charge to decay to 50% of its initial value in 40 cycles? Assume 𝜔=𝜔.


In an oscillating RLC circuit, 𝑅=7.0Ω, 𝐿=10mH, and 𝐶=3.0µF. Initially, the capacitor has a charge of 8.0 µC and the current is zero.

Calculate the charge on the capacitor 10 cycles later.

Calculate the charge on the capacitor 60 cycles later.

  • A12×10 C
  • B41×10 C
  • C9.1×10 C
  • D7.2×10 C
  • E5.1×10 C

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