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 = 10 kΩt = 0C22 µF+−vC​vC​(0) = 9 V

The capacitor has been charged to 9 V. At t = 0 the switch closes and the capacitor discharges through R. Find the capacitor voltage vC at t = 400 ms.

vC(0) = 9 VR = 10 kΩC = 22 µFt = 400 ms
vC = V
2.Easy
+−Vs​20 Vt = 0R = 2.2 kΩC22 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 80 ms.

Vs = 20 VR = 2.2 kΩC = 22 µFt = 80 ms
vC = V
3.Medium
+−Vs​20 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 = 20 VR = 15 ΩL = 100 mHt = 10 ms
i = A
4.Medium
+−Vs​20 Vt = 0R = 20 ΩL220 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 = 20 VR = 20 ΩL = 220 mH
W(∞) = mJ
5.Hard
+−Vs​6 Vt = 0R = 4.7 kΩC47 µF+−vC​vC​(0) = 10 V

Just before the switch closes at t = 0, the capacitor holds 10 V with the polarity shown. Find the capacitor voltage vC at t = 100 ms.

Vs = 6 VR = 4.7 kΩC = 47 µFvC(0) = 10 Vt = 100 ms
vC = V
6.Hard
+−Vs​24 Vt = 0R = 6.8 kΩC10 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 18.6 V? Find t.

Vs = 24 VR = 6.8 kΩC = 10 µFvC(0) = 15 V
t = ms

Answer key

  1. 1. vC = 1.461 V
  2. 2. vC = 16.17 V
  3. 3. i = 1.036 A
  4. 4. W(∞) = 110 mJ
  5. 5. vC = 8.544 V
  6. 6. t = 34.74 ms

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