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​12 Vt = 0R = 4.7 kΩC22 µF+−vC​

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

Vs = 12 VR = 4.7 kΩC = 22 µF
τ = ms
2.Easy
+−Vs​5 Vt = 0R = 6.8 kΩC47 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 80 ms.

Vs = 5 VR = 6.8 kΩC = 47 µFt = 80 ms
vC = V
3.Medium
+−Vs​15 Vt = 0R = 5 ΩL10 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the energy W stored in the inductor at t = 5 ms, in mJ.

Vs = 15 VR = 5 ΩL = 10 mHt = 5 ms
W = mJ
4.Medium
+−Vs​5 Vt = 0R = 10 ΩL22 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the voltage vL across the inductor at t = 5 ms.

Vs = 5 VR = 10 ΩL = 22 mHt = 5 ms
vL = V
5.Hard
+−Vs​24 VR1​ = 5 ΩR2​ = 33 Ωopens at t = 0L33 mHi(t)

The switch across R2 has been closed for a long time, so the inductor current is steady. At t = 0 the switch opens. Find the inductor current i at t = 1 ms.

Vs = 24 VR1 = 5 ΩR2 = 33 ΩL = 33 mHt = 1 ms
i = A
6.Hard
+−Vs​9 Vopens at t = 0R1​ = 10 kΩR2​ = 2.2 kΩi2​C100 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 current i2 through R2 at t = 200 ms.

Vs = 9 VR1 = 10 kΩR2 = 2.2 kΩC = 100 µFt = 200 ms
i2 = mA

Answer key

  1. 1. τ = 103.4 ms
  2. 2. vC = 1.107 V
  3. 3. W = 37.92 mJ
  4. 4. vL = 0.5152 V
  5. 5. i = 1.949 A
  6. 6. i2 = 0.2972 mA

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