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​10 Vt = 0R = 6.8 kΩC33 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 60 ms.

Vs = 10 VR = 6.8 kΩC = 33 µFt = 60 ms
vC = V
2.Easy
R = 1 kΩt = 0C68 µF+−vC​vC​(0) = 6 V

The capacitor has been charged to 6 V. At t = 0 the switch closes and the capacitor discharges through R. How long does it take for vC to fall to 4.5 V? Find t.

vC(0) = 6 VR = 1 kΩC = 68 µF
t = ms
3.Medium
R = 50 Ωt = 0L33 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 = 1 ms.

i(0) = 3 AR = 50 ΩL = 33 mHt = 1 ms
vR = V
4.Medium
+−Vs​5 Vt = 0R = 50 ΩL100 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the voltage vL across the inductor at t = 5 ms.

Vs = 5 VR = 50 ΩL = 100 mHt = 5 ms
vL = V
5.Hard
+−Vs​10 Vt = 0R = 1 kΩC47 µF+−vC​vC​(0) = 15 V

Just before the switch closes at t = 0, the capacitor holds 15 V with the polarity shown. How long does it take for vC to reach 12.5 V? Find t.

Vs = 10 VR = 1 kΩC = 47 µFvC(0) = 15 V
t = ms
6.Hard
+−Vs​20 Vt = 0R = 3.3 kΩC33 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 14 V? Find t.

Vs = 20 VR = 3.3 kΩC = 33 µFvC(0) = 8 V
t = ms

Answer key

  1. 1. vC = 2.346 V
  2. 2. t = 19.56 ms
  3. 3. vR = 32.97 V
  4. 4. vL = 0.4104 V
  5. 5. t = 32.58 ms
  6. 6. t = 75.48 ms

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