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​24 Vt = 0R = 3.3 kΩC10 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. How long after the switch closes does the capacitor voltage reach 90% of its final value? Find t.

Vs = 24 VR = 3.3 kΩC = 10 µF
t = ms
2.Easy
+−Vs​10 Vt = 0R = 10 kΩC33 µF+−vC​i

The capacitor is uncharged when the switch closes at t = 0. Find the charging current i at t = 100 ms.

Vs = 10 VR = 10 kΩC = 33 µFt = 100 ms
i = mA
3.Medium
+−Vs​6 Vt = 0R = 15 ΩL22 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 = 6 VR = 15 ΩL = 22 mHt = 1 ms
vL = V
4.Medium
+−Vs​9 Vt = 0R1​ = 4.7 kΩR2​ = 10 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 time constant τ of the circuit after the switch closes.

Vs = 9 VR1 = 4.7 kΩR2 = 10 kΩC = 100 µF
τ = ms
5.Hard
+−Vs​5 Vt = 0R = 3.3 kΩC220 µF+−vC​vC​(0) = 12 V

Just before the switch closes at t = 0, the capacitor holds 12 V with the polarity shown. Find the capacitor voltage vC at t = 1000 ms.

Vs = 5 VR = 3.3 kΩC = 220 µFvC(0) = 12 Vt = 1000 ms
vC = V
6.Hard
+−Vs​20 Vt = 0R = 1 kΩC68 µF+−vC​vC​(0) = 12 V

Just before the switch closes at t = 0, the capacitor holds 12 V with the polarity shown. Find the capacitor voltage vC at t = 20 ms.

Vs = 20 VR = 1 kΩC = 68 µFvC(0) = 12 Vt = 20 ms
vC = V

Answer key

  1. 1. t = 75.99 ms
  2. 2. i = 0.7386 mA
  3. 3. vL = 3.034 V
  4. 4. τ = 319.7 ms
  5. 5. vC = 6.766 V
  6. 6. vC = 14.04 V

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