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 = 2.2 kΩC220 µF+−vC​

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

Vs = 6 VR = 2.2 kΩC = 220 µFt = 150 ms
vR = V
2.Easy
+−Vs​12 Vt = 0R = 3.3 kΩC100 µF+−vC​

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

Vs = 12 VR = 3.3 kΩC = 100 µF
τ = ms
3.Medium
+−Vs​9 Vt = 0R = 22 ΩL68 mHi(t)

The inductor carries no current before the switch closes at t = 0. How long after the switch closes does the current reach 50% of its final value? Find t.

Vs = 9 VR = 22 ΩL = 68 mH
t = ms
4.Medium
R = 20 Ωt = 0L100 mHi(t)

The inductor carries a steady current of 2 A. At t = 0 the switch closes the loop through R and the source is removed, so the inductor current decays through R. Find the current i at t = 10 ms.

i(0) = 2 AR = 20 ΩL = 100 mHt = 10 ms
i = A
5.Hard
+−Vs​20 Vt = 0R = 10 kΩC47 µF+−vC​vC​(0) = 15 V

Just before the switch closes at t = 0, the capacitor holds 15 V with the polarity shown. Find the capacitor voltage vC at t = 150 ms.

Vs = 20 VR = 10 kΩC = 47 µFvC(0) = 15 Vt = 150 ms
vC = V
6.Hard
+−Vs​24 VR1​ = 10 ΩR2​ = 47 Ωcloses at t = 0L150 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. How long after t = 0 does the inductor current reach 1.608 A? Find t.

Vs = 24 VR1 = 10 ΩR2 = 47 ΩL = 150 mH
t = ms

Answer key

  1. 1. vR = 4.401 V
  2. 2. τ = 330 ms
  3. 3. t = 2.142 ms
  4. 4. i = 0.2707 A
  5. 5. vC = 16.37 V
  6. 6. t = 13.74 ms

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