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​5 Vt = 0R = 1 kΩC22 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 15 ms.

Vs = 5 VR = 1 kΩC = 22 µFt = 15 ms
vC = V
2.Easy
R = 4.7 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 5 V? Find t.

vC(0) = 20 VR = 4.7 kΩC = 220 µF
t = ms
3.Medium
R = 100 Ωt = 0L47 mHi(t)

The inductor carries a steady current of 2 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 1 A? Find t.

i(0) = 2 AR = 100 ΩL = 47 mH
t = ms
4.Medium
+−Vs​6 Vt = 0R = 50 ΩL10 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 = 6 VR = 50 ΩL = 10 mH
W(∞) = mJ
5.Hard
+−Vs​6 Vopens at t = 0R1​ = 3.3 kΩR2​ = 4.7 kΩC33 µF+−vC​

The switch has been closed for a long time, so the circuit is in steady state. At t = 0 the switch opens. Find the capacitor voltage vC at t = 50 ms.

Vs = 6 VR1 = 3.3 kΩR2 = 4.7 kΩC = 33 µFt = 50 ms
vC = V
6.Hard
+−Vs​6 Vt = 0R = 3.3 kΩC22 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 = 60 ms.

Vs = 6 VR = 3.3 kΩC = 22 µFvC(0) = 5 Vt = 60 ms
vC = V

Answer key

  1. 1. vC = 2.472 V
  2. 2. t = 1433 ms
  3. 3. t = 0.3258 ms
  4. 4. W(∞) = 0.072 mJ
  5. 5. vC = 2.554 V
  6. 6. vC = 5.562 V

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