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 = 1 kΩC100 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 100 ms.

Vs = 12 VR = 1 kΩC = 100 µFt = 100 ms
vC = V
2.Easy
R = 1 kΩt = 0C68 µF+−vC​vC​(0) = 20 V

The capacitor has been charged to 20 V. At t = 0 the switch closes and the capacitor discharges through R. How long does it take for vC to fall to 10 V? Find t.

vC(0) = 20 VR = 1 kΩC = 68 µF
t = ms
3.Medium
+−Vs​15 Vt = 0R1​ = 1 kΩR2​ = 3.3 kΩC10 µF+−vC​

The source Vₛ charges the capacitor through R₁, and R₂ is connected in parallel with C. The capacitor is uncharged when the switch closes at t = 0. Find the time constant τ of the circuit after the switch closes.

Vs = 15 VR1 = 1 kΩR2 = 3.3 kΩC = 10 µF
τ = ms
4.Medium
+−Vs​9 Vt = 0R = 22 ΩL100 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the energy W stored in the inductor at t = 5 ms, in mJ.

Vs = 9 VR = 22 ΩL = 100 mHt = 5 ms
W = mJ
5.Hard
+−Vs​12 Vt = 0R = 10 kΩC220 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 13.2 V? Find t.

Vs = 12 VR = 10 kΩC = 220 µFvC(0) = 15 V
t = ms
6.Hard
+−Vs​15 Vt = 0R = 1 kΩC47 µF+−vC​vC​(0) = 5 V

Just before the switch closes at t = 0, the capacitor holds 5 V with the polarity shown. How long does it take for vC to reach 10 V? Find t.

Vs = 15 VR = 1 kΩC = 47 µFvC(0) = 5 V
t = ms

Answer key

  1. 1. vC = 7.585 V
  2. 2. t = 47.13 ms
  3. 3. τ = 7.674 ms
  4. 4. W = 3.724 mJ
  5. 5. t = 2016 ms
  6. 6. t = 32.58 ms

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