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.

Q1:

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?

Q2:

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

Q3:

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.

Q4:

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.

  • A 1 2 × 1 0 C
  • B 4 1 × 1 0 C
  • C 9 . 1 × 1 0 C
  • D 7 . 2 × 1 0 C
  • E 5 . 1 × 1 0 C

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