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 = 3.3 kΩC33 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the time constant τ of the circuit.

Vs = 5 VR = 3.3 kΩC = 33 µF
τ = ms
2.Easy
+−Vs​9 Vt = 0R = 2.2 kΩC10 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. How long after the switch closes does the capacitor voltage reach 50% of its final value? Find t.

Vs = 9 VR = 2.2 kΩC = 10 µF
t = ms
3.Medium
+−Vs​10 Vt = 0R = 47 ΩL220 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the current i at t = 5 ms.

Vs = 10 VR = 47 ΩL = 220 mHt = 5 ms
i = A
4.Medium
R = 10 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 0.5 A? Find t.

i(0) = 2 AR = 10 ΩL = 47 mH
t = ms
5.Hard
+−Vs​24 Vt = 0R = 1 kΩC47 µF+−vC​vC​(0) = 6 V

Just before the switch closes at t = 0, the capacitor holds 6 V with the polarity shown. Find the capacitor voltage vC at t = 15 ms.

Vs = 24 VR = 1 kΩC = 47 µFvC(0) = 6 Vt = 15 ms
vC = V
6.Hard
+−Vs​15 Vt = 0R = 4.7 kΩC47 µF+−vC​vC​(0) = 4 V

Just before the switch closes at t = 0, the capacitor holds 4 V with the polarity shown. How long does it take for vC to reach 9.5 V? Find t.

Vs = 15 VR = 4.7 kΩC = 47 µFvC(0) = 4 V
t = ms

Answer key

  1. 1. τ = 108.9 ms
  2. 2. t = 15.25 ms
  3. 3. i = 0.1397 A
  4. 4. t = 6.516 ms
  5. 5. vC = 10.92 V
  6. 6. t = 153.1 ms

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