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​6 Vt = 0R = 6.8 kΩC10 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. How long after the switch closes does the capacitor voltage reach 80% of its final value? Find t.

Vs = 6 VR = 6.8 kΩC = 10 µF
t = ms
2.Easy
+−Vs​10 Vt = 0R = 1 kΩC68 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 75 ms.

Vs = 10 VR = 1 kΩC = 68 µFt = 75 ms
vC = V
3.Medium
+−Vs​6 Vt = 0R = 20 ΩL220 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the voltage vL across the inductor at t = 30 ms.

Vs = 6 VR = 20 ΩL = 220 mHt = 30 ms
vL = V
4.Medium
R = 22 Ωt = 0L47 mHi(t)

The inductor carries a steady current of 1.5 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) = 1.5 AR = 22 ΩL = 47 mHt = 5 ms
vR = V
5.Hard
+−Vs​9 Vt = 0R = 10 kΩC22 µF+−vC​vC​(0) = 3 V

Just before the switch closes at t = 0, the capacitor holds 3 V with the polarity shown. How long does it take for vC to reach 6.6 V? Find t.

Vs = 9 VR = 10 kΩC = 22 µFvC(0) = 3 V
t = ms
6.Hard
+−Vs​9 Vt = 0R = 1 kΩC100 µF+−vC​vC​(0) = 12 V

Just before the switch closes at t = 0, the capacitor holds 12 V with the polarity shown. Find the capacitor voltage vC at t = 200 ms.

Vs = 9 VR = 1 kΩC = 100 µFvC(0) = 12 Vt = 200 ms
vC = V

Answer key

  1. 1. t = 109.4 ms
  2. 2. vC = 6.681 V
  3. 3. vL = 0.3924 V
  4. 4. vR = 3.177 V
  5. 5. t = 201.6 ms
  6. 6. vC = 9.406 V

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