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​15 Vt = 0R = 6.8 kΩC33 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 200 ms.

Vs = 15 VR = 6.8 kΩC = 33 µFt = 200 ms
vC = V
2.Easy
+−Vs​10 Vt = 0R = 3.3 kΩC10 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the voltage vR across the resistor at t = 25 ms.

Vs = 10 VR = 3.3 kΩC = 10 µFt = 25 ms
vR = V
3.Medium
+−Vs​9 Vt = 0R = 20 ΩL33 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 = 9 VR = 20 ΩL = 33 mH
W(∞) = mJ
4.Medium
R = 22 Ωt = 0L150 mHi(t)

The inductor carries a steady current of 0.5 A. At t = 0 the switch closes the loop through R and the source is removed, so the inductor current decays through R. How long does it take for the current to fall to 0.25 A? Find t.

i(0) = 0.5 AR = 22 ΩL = 150 mH
t = ms
5.Hard
+−Vs​6 VR1​ = 10 ΩR2​ = 10 Ωopens at t = 0L220 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 = 25 ms.

Vs = 6 VR1 = 10 ΩR2 = 10 ΩL = 220 mHt = 25 ms
i = A
6.Hard
+−Vs​12 Vt = 0R = 6.8 kΩC47 µF+−vC​vC​(0) = 5 V

Just before the switch closes at t = 0, the capacitor holds 5 V with the polarity shown. Find the capacitor voltage vC at t = 100 ms.

Vs = 12 VR = 6.8 kΩC = 47 µFvC(0) = 5 Vt = 100 ms
vC = V

Answer key

  1. 1. vC = 8.848 V
  2. 2. vR = 4.688 V
  3. 3. W(∞) = 3.341 mJ
  4. 4. t = 4.726 ms
  5. 5. i = 0.3309 A
  6. 6. vC = 6.881 V

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