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 = 10 kΩC10 µF+−vC​i

The capacitor is uncharged when the switch closes at t = 0. Find the current i(0⁺) just after the switch closes.

Vs = 24 VR = 10 kΩC = 10 µF
i(0⁺) = mA
2.Easy
R = 1 kΩt = 0C33 µF+−vC​vC​(0) = 24 V

The capacitor has been charged to 24 V. At t = 0 the switch closes and the capacitor discharges through R. How long does it take for vC to fall to 18 V? Find t.

vC(0) = 24 VR = 1 kΩC = 33 µF
t = ms
3.Medium
+−Vs​15 Vt = 0R1​ = 3.3 kΩR2​ = 3.3 kΩC47 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 = 80 ms.

Vs = 15 VR1 = 3.3 kΩR2 = 3.3 kΩC = 47 µFt = 80 ms
vC = V
4.Medium
+−Vs​9 Vt = 0R = 22 ΩL220 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the energy W stored in the inductor at t = 15 ms, in mJ.

Vs = 9 VR = 22 ΩL = 220 mHt = 15 ms
W = mJ
5.Hard
+−Vs​12 Vt = 0R = 6.8 kΩC100 µF+−vC​vC​(0) = 4 V

Just before the switch closes at t = 0, the capacitor holds 4 V with the polarity shown. Find the capacitor voltage vC at t = 200 ms.

Vs = 12 VR = 6.8 kΩC = 100 µFvC(0) = 4 Vt = 200 ms
vC = V
6.Hard
+−Vs​5 Vt = 0R = 1 kΩC22 µF+−vC​vC​(0) = 12 V

Just before the switch closes at t = 0, the capacitor holds 12 V with the polarity shown. How long does it take for vC to reach 7.8 V? Find t.

Vs = 5 VR = 1 kΩC = 22 µFvC(0) = 12 V
t = ms

Answer key

  1. 1. i(0⁺) = 2.4 mA
  2. 2. t = 9.494 ms
  3. 3. vC = 4.827 V
  4. 4. W = 11.11 mJ
  5. 5. vC = 6.038 V
  6. 6. t = 20.16 ms

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