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 = 2.2 kΩC100 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 60 ms.

Vs = 5 VR = 2.2 kΩC = 100 µFt = 60 ms
vC = V
2.Easy
R = 2.2 kΩt = 0C220 µF+−vC​vC​(0) = 12 V

The capacitor has been charged to 12 V. At t = 0 the switch closes and the capacitor discharges through R. Find the capacitor voltage vC at t = 200 ms.

vC(0) = 12 VR = 2.2 kΩC = 220 µFt = 200 ms
vC = V
3.Medium
+−Vs​24 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 at t = 1 ms, in mJ.

Vs = 24 VR = 47 ΩL = 33 mHt = 1 ms
W = mJ
4.Medium
+−Vs​15 Vt = 0R = 50 ΩL47 mHi(t)

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

Vs = 15 VR = 50 ΩL = 47 mHt = 1 ms
vL = V
5.Hard
+−Vs​5 Vt = 0R = 6.8 kΩC47 µF+−vC​vC​(0) = 30 V

Just before the switch closes at t = 0, the capacitor holds 30 V with the polarity shown. How long does it take for vC to reach 12.5 V? Find t.

Vs = 5 VR = 6.8 kΩC = 47 µFvC(0) = 30 V
t = ms
6.Hard
+−Vs​12 VR1​ = 10 ΩR2​ = 22 Ωcloses at t = 0L100 mHi(t)

The switch across R2 has been open for a long time, so the inductor current is steady. At t = 0 the switch closes and shorts out R2. Find the inductor current i at t = 25 ms.

Vs = 12 VR1 = 10 ΩR2 = 22 ΩL = 100 mHt = 25 ms
i = A

Answer key

  1. 1. vC = 1.193 V
  2. 2. vC = 7.938 V
  3. 3. W = 2.481 mJ
  4. 4. vL = 5.177 V
  5. 5. t = 384.8 ms
  6. 6. i = 1.132 A

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