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
R = 1 kΩt = 0C10 µF+−vC​vC​(0) = 10 V

The capacitor has been charged to 10 V. At t = 0 the switch closes and the capacitor discharges through R. Find the capacitor voltage vC at t = 25 ms.

vC(0) = 10 VR = 1 kΩC = 10 µFt = 25 ms
vC = V
2.Easy
+−Vs​20 Vt = 0R = 2.2 kΩC33 µF+−vC​

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

Vs = 20 VR = 2.2 kΩC = 33 µFt = 120 ms
vR = V
3.Medium
+−Vs​24 Vt = 0R1​ = 3.3 kΩR2​ = 4.7 kΩC100 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 = 24 VR1 = 3.3 kΩR2 = 4.7 kΩC = 100 µFt = 150 ms
vC = V
4.Medium
+−Vs​12 Vt = 0R = 10 ΩL150 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 = 12 VR = 10 ΩL = 150 mH
W(∞) = mJ
5.Hard
+−Vs​30 Vopens at t = 0R1​ = 6.8 kΩR2​ = 10 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 = 750 ms.

Vs = 30 VR1 = 6.8 kΩR2 = 10 kΩC = 33 µFt = 750 ms
vC = V
6.Hard
+−Vs​9 Vt = 0R = ?C22 µF+−vC​

A timer starts charging an uncharged capacitor through a resistor from a 9 V supply at t = 0. It must trigger when the capacitor voltage reaches 8.1 V, exactly 20 ms after the start. With C = 22 µF, find the resistance R needed.

Vs = 9 VVth = 8.1 VT = 20 msC = 22 µF
R = kΩ

Answer key

  1. 1. vC = 0.8208 V
  2. 2. vR = 3.83 V
  3. 3. vC = 7.596 V
  4. 4. W(∞) = 108 mJ
  5. 5. vC = 1.84 V
  6. 6. R = 0.3948 kΩ

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