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
R = 1 kΩt = 0C220 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 8 V? Find t.

vC(0) = 20 VR = 1 kΩC = 220 µF
t = ms
2.Easy
R = 10 kΩt = 0C220 µF+−vC​vC​(0) = 15 V

The capacitor has been charged to 15 V. At t = 0 the switch closes and the capacitor discharges through R. Find the capacitor voltage vC at t = 1000 ms.

vC(0) = 15 VR = 10 kΩC = 220 µFt = 1000 ms
vC = V
3.Medium
+−Vs​15 Vt = 0R1​ = 1 kΩR2​ = 6.8 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 capacitor voltage vC at t = 10 ms.

Vs = 15 VR1 = 1 kΩR2 = 6.8 kΩC = 10 µFt = 10 ms
vC = V
4.Medium
+−Vs​12 Vt = 0R = 15 ΩL100 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the current i at t = 10 ms.

Vs = 12 VR = 15 ΩL = 100 mHt = 10 ms
i = A
5.Hard
+−Vs​10 Vt = 0R = 4.7 kΩC33 µF+−vC​vC​(0) = 2 V

Just before the switch closes at t = 0, the capacitor holds 2 V with the polarity shown. Find the capacitor voltage vC at t = 300 ms.

Vs = 10 VR = 4.7 kΩC = 33 µFvC(0) = 2 Vt = 300 ms
vC = V
6.Hard
+−Vs​9 Vt = 0R = 6.8 kΩC220 µF+−vC​vC​(0) = 20 V

Just before the switch closes at t = 0, the capacitor holds 20 V with the polarity shown. How long does it take for vC to reach 12.3 V? Find t.

Vs = 9 VR = 6.8 kΩC = 220 µFvC(0) = 20 V
t = ms

Answer key

  1. 1. t = 201.6 ms
  2. 2. vC = 9.521 V
  3. 3. vC = 8.924 V
  4. 4. i = 0.6215 A
  5. 5. vC = 8.844 V
  6. 6. t = 1801 ms

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