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​24 Vt = 0R = 3.3 kΩC33 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 120 ms.

Vs = 24 VR = 3.3 kΩC = 33 µFt = 120 ms
vC = V
2.Easy
+−Vs​24 Vt = 0R = 10 kΩC10 µF+−vC​

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

Vs = 24 VR = 10 kΩC = 10 µF
τ = ms
3.Medium
+−Vs​12 Vt = 0R = 68 ΩL33 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the current i at t = 1 ms.

Vs = 12 VR = 68 ΩL = 33 mHt = 1 ms
i = A
4.Medium
+−Vs​5 Vt = 0R = 5 ΩL68 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the energy W(∞) stored in the inductor once the circuit has settled, in mJ.

Vs = 5 VR = 5 ΩL = 68 mH
W(∞) = mJ
5.Hard
+−Vs​9 Vt = 0R = 4.7 kΩC100 µF+−vC​vC​(0) = 3 V

Just before the switch closes at t = 0, the capacitor holds 3 V with the polarity shown. Find the capacitor voltage vC at t = 1000 ms.

Vs = 9 VR = 4.7 kΩC = 100 µFvC(0) = 3 Vt = 1000 ms
vC = V
6.Hard
+−Vs​24 Vt = 0R = 2.2 kΩC68 µF+−vC​vC​(0) = 18 V

Just before the switch closes at t = 0, the capacitor holds 18 V with the polarity shown. How long does it take for vC to reach 19.8 V? Find t.

Vs = 24 VR = 2.2 kΩC = 68 µFvC(0) = 18 V
t = ms

Answer key

  1. 1. vC = 16.03 V
  2. 2. τ = 100 ms
  3. 3. i = 0.154 A
  4. 4. W(∞) = 34 mJ
  5. 5. vC = 8.285 V
  6. 6. t = 53.36 ms

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