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​20 Vt = 0R = 1 kΩC47 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the voltage vR across the resistor at t = 30 ms.

Vs = 20 VR = 1 kΩC = 47 µFt = 30 ms
vR = V
2.Easy
+−Vs​5 Vt = 0R = 2.2 kΩC47 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 150 ms.

Vs = 5 VR = 2.2 kΩC = 47 µFt = 150 ms
vC = V
3.Medium
+−Vs​24 Vt = 0R = 47 ΩL68 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the current i at t = 1 ms.

Vs = 24 VR = 47 ΩL = 68 mHt = 1 ms
i = A
4.Medium
+−Vs​12 Vt = 0R = 47 ΩL33 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 = 47 ΩL = 33 mH
W(∞) = mJ
5.Hard
+−Vs​24 Vt = 0R = 10 kΩC22 µF+−vC​vC​(0) = 12 V

Just before the switch closes at t = 0, the capacitor holds 12 V with the polarity shown. How long does it take for vC to reach 20.4 V? Find t.

Vs = 24 VR = 10 kΩC = 22 µFvC(0) = 12 V
t = ms
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 5.69 V, exactly 1000 ms after the start. With C = 22 µF, find the resistance R needed.

Vs = 9 VVth = 5.69 VT = 1000 msC = 22 µF
R = kΩ

Answer key

  1. 1. vR = 10.56 V
  2. 2. vC = 3.828 V
  3. 3. i = 0.2548 A
  4. 4. W(∞) = 1.076 mJ
  5. 5. t = 264.9 ms
  6. 6. R = 45.44 kΩ

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