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​9 Vt = 0R = 6.8 kΩC22 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 60 ms.

Vs = 9 VR = 6.8 kΩC = 22 µFt = 60 ms
vC = V
2.Easy
+−Vs​6 Vt = 0R = 4.7 kΩC33 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 = 6 VR = 4.7 kΩC = 33 µF
i(0⁺) = mA
3.Medium
+−Vs​15 Vt = 0R = 22 ΩL47 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 = 15 VR = 22 ΩL = 47 mH
W(∞) = mJ
4.Medium
R = 15 Ωt = 0L100 mHi(t)

The inductor carries a steady current of 2.5 A. At t = 0 the switch closes the loop through R and the source is removed, so the inductor current decays through R. Find the voltage vR across R at t = 5 ms.

i(0) = 2.5 AR = 15 ΩL = 100 mHt = 5 ms
vR = V
5.Hard
+−Vs​12 VR1​ = 5 ΩR2​ = 47 Ωopens at t = 0L100 mHi(t)

The switch across R2 has been closed for a long time, so the inductor current is steady. At t = 0 the switch opens. Find the inductor current i at t = 5 ms.

Vs = 12 VR1 = 5 ΩR2 = 47 ΩL = 100 mHt = 5 ms
i = A
6.Hard
+−Vs​12 Vt = 0R = 6.8 kΩC220 µF+−vC​vC​(0) = 8 V

Just before the switch closes at t = 0, the capacitor holds 8 V with the polarity shown. Find the capacitor voltage vC at t = 1000 ms.

Vs = 12 VR = 6.8 kΩC = 220 µFvC(0) = 8 Vt = 1000 ms
vC = V

Answer key

  1. 1. vC = 2.974 V
  2. 2. i(0⁺) = 1.277 mA
  3. 3. W(∞) = 10.92 mJ
  4. 4. vR = 17.71 V
  5. 5. i = 0.3919 A
  6. 6. vC = 9.95 V

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