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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
+−Vs​9 Vt = 0R = 1 kΩC220 µF+−vC​

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

Vs = 9 VR = 1 kΩC = 220 µF
τ = ms
2.Easy
+−Vs​12 Vt = 0R = 4.7 kΩC22 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 120 ms.

Vs = 12 VR = 4.7 kΩC = 22 µFt = 120 ms
vC = V
3.Medium
+−Vs​30 Vt = 0R1​ = 1 kΩR2​ = 10 kΩC68 µF+−vC​

The source Vₛ charges the capacitor through R₁, and R₂ is connected in parallel with C. The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 150 ms.

Vs = 30 VR1 = 1 kΩR2 = 10 kΩC = 68 µFt = 150 ms
vC = V
4.Medium
R = 15 Ωt = 0L100 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. Find the voltage vR across R at t = 10 ms.

i(0) = 2 AR = 15 ΩL = 100 mHt = 10 ms
vR = V
5.Hard
+−Vs​12 Vt = 0R = 2.2 kΩC10 µF+−vC​vC​(0) = 10 V

Just before the switch closes at t = 0, the capacitor holds 10 V with the polarity shown. How long does it take for vC to reach 11 V? Find t.

Vs = 12 VR = 2.2 kΩC = 10 µFvC(0) = 10 V
t = ms
6.Hard
+−Vs​15 Vopens at t = 0R1​ = 3.3 kΩR2​ = 1 kΩC220 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 = 100 ms.

Vs = 15 VR1 = 3.3 kΩR2 = 1 kΩC = 220 µFt = 100 ms
vC = V

Answer key

  1. 1. τ = 220 ms
  2. 2. vC = 8.24 V
  3. 3. vC = 24.86 V
  4. 4. vR = 6.694 V
  5. 5. t = 15.25 ms
  6. 6. vC = 2.214 V

Full step-by-step solutions: practise this topic on examproblems.com.