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 = 3.3 kΩC22 µF+−vC​

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

Vs = 15 VR = 3.3 kΩC = 22 µF
τ = ms
2.Easy
+−Vs​9 Vt = 0R = 3.3 kΩC47 µF+−vC​

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

Vs = 9 VR = 3.3 kΩC = 47 µFt = 200 ms
vC = V
3.Medium
+−Vs​12 Vt = 0R = 22 ΩL22 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the energy W stored in the inductor at t = 1 ms, in mJ.

Vs = 12 VR = 22 ΩL = 22 mHt = 1 ms
W = mJ
4.Medium
+−Vs​24 Vt = 0R = 33 ΩL220 mHi(t)

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

Vs = 24 VR = 33 ΩL = 220 mHt = 5 ms
vL = V
5.Hard
+−Vs​6 Vopens at t = 0R1​ = 1 kΩR2​ = 3.3 kΩC22 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 = 1 kΩR2 = 3.3 kΩC = 22 µFt = 50 ms
vC = V
6.Hard
+−Vs​9 VR1​ = 20 ΩR2​ = 10 Ωopens at t = 0L33 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 = 1 ms.

Vs = 9 VR1 = 20 ΩR2 = 10 ΩL = 33 mHt = 1 ms
i = A

Answer key

  1. 1. τ = 72.6 ms
  2. 2. vC = 6.521 V
  3. 3. W = 1.308 mJ
  4. 4. vL = 11.34 V
  5. 5. vC = 2.313 V
  6. 6. i = 0.3604 A

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