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​6 Vt = 0R = 10 kΩC47 µF+−vC​

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

Vs = 6 VR = 10 kΩC = 47 µFt = 120 ms
vC = V
2.Easy
+−Vs​6 Vt = 0R = 3.3 kΩC47 µF+−vC​

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

Vs = 6 VR = 3.3 kΩC = 47 µF
τ = ms
3.Medium
R = 22 Ωt = 0L150 mHi(t)

The inductor carries a steady current of 1.5 A. At t = 0 the switch closes the loop through R and the source is removed, so the inductor current decays through R. How long does it take for the current to fall to 0.3 A? Find t.

i(0) = 1.5 AR = 22 ΩL = 150 mH
t = ms
4.Medium
+−Vs​9 Vt = 0R = 33 ΩL10 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 = 9 VR = 33 ΩL = 10 mHt = 1 ms
vL = V
5.Hard
+−Vs​15 Vt = 0R = 10 kΩC?+−vC​

A timer starts charging an uncharged capacitor through a resistor from a 15 V supply at t = 0. It must trigger when the capacitor voltage reaches 9 V, exactly 250 ms after the start. With R = 10 kΩ, find the capacitance C needed.

Vs = 15 VVth = 9 VT = 250 msR = 10 kΩ
C = µF
6.Hard
+−Vs​12 Vt = 0R = ?C100 µF+−vC​

A timer starts charging an uncharged capacitor through a resistor from a 12 V supply at t = 0. It must trigger when the capacitor voltage reaches 6 V, exactly 200 ms after the start. With C = 100 µF, find the resistance R needed.

Vs = 12 VVth = 6 VT = 200 msC = 100 µF
R = kΩ

Answer key

  1. 1. vC = 1.352 V
  2. 2. τ = 155.1 ms
  3. 3. t = 10.97 ms
  4. 4. vL = 0.3319 V
  5. 5. C = 27.28 µF
  6. 6. R = 2.885 kΩ

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