RC & RL transients worksheet with answers

Free printable RC & RL transients worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
+−Vs​12 Vt = 0R = 4.7 kΩC220 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 750 ms.

Vs = 12 VR = 4.7 kΩC = 220 µFt = 750 ms
vC = V
2.Easy
+−Vs​9 Vt = 0R = 3.3 kΩC100 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the time constant τ of the circuit.

Vs = 9 VR = 3.3 kΩC = 100 µF
τ = ms
3.Medium
+−Vs​5 Vt = 0R = 68 ΩL68 mHi(t)

The inductor carries no current before the switch closes at t = 0. How long after the switch closes does the current reach 99% of its final value? Find t.

Vs = 5 VR = 68 ΩL = 68 mH
t = ms
4.Medium
R = 33 Ωt = 0L100 mHi(t)

The inductor carries a steady current of 3 A. At t = 0 the switch closes the loop through R and the source is removed, so the inductor current decays through R. Find the voltage vR across R at t = 5 ms.

i(0) = 3 AR = 33 ΩL = 100 mHt = 5 ms
vR = V
5.Hard
+−Vs​5 Vt = 0R = 1 kΩC10 µF+−vC​vC​(0) = 8 V

Just before the switch closes at t = 0, the capacitor holds 8 V with the polarity shown. How long does it take for vC to reach 6.5 V? Find t.

Vs = 5 VR = 1 kΩC = 10 µFvC(0) = 8 V
t = ms
6.Hard
+−Vs​15 Vt = 0R = ?C2.2 µF+−vC​

A timer starts charging an uncharged capacitor through a resistor from a 15 V supply at t = 0. It must trigger when the capacitor voltage reaches 13.5 V, exactly 20 ms after the start. With C = 2.2 µF, find the resistance R needed.

Vs = 15 VVth = 13.5 VT = 20 msC = 2.2 µF
R = kΩ

Answer key

  1. 1. vC = 6.19 V
  2. 2. τ = 330 ms
  3. 3. t = 4.605 ms
  4. 4. vR = 19.01 V
  5. 5. t = 6.931 ms
  6. 6. R = 3.948 kΩ

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