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 = 6.8 kΩC47 µF+−vC​

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

Vs = 24 VR = 6.8 kΩC = 47 µF
τ = ms
2.Easy
+−Vs​12 Vt = 0R = 1 kΩC47 µF+−vC​i

The capacitor is uncharged when the switch closes at t = 0. Find the current i(0⁺) just after the switch closes.

Vs = 12 VR = 1 kΩC = 47 µF
i(0⁺) = mA
3.Medium
+−Vs​10 Vt = 0R1​ = 10 kΩR2​ = 3.3 kΩC22 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 = 10 VR1 = 10 kΩR2 = 3.3 kΩC = 22 µF
τ = ms
4.Medium
+−Vs​12 Vt = 0R = 68 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 = 12 VR = 68 ΩL = 10 mHt = 1 ms
vL = V
5.Hard
+−Vs​15 Vt = 0R = ?C47 µF+−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 13.5 V, exactly 1000 ms after the start. With C = 47 µF, find the resistance R needed.

Vs = 15 VVth = 13.5 VT = 1000 msC = 47 µF
R = kΩ
6.Hard
+−Vs​6 Vt = 0R = 2.2 kΩC33 µF+−vC​vC​(0) = 10 V

Just before the switch closes at t = 0, the capacitor holds 10 V with the polarity shown. How long does it take for vC to reach 6.8 V? Find t.

Vs = 6 VR = 2.2 kΩC = 33 µFvC(0) = 10 V
t = ms

Answer key

  1. 1. τ = 319.6 ms
  2. 2. i(0⁺) = 12 mA
  3. 3. τ = 54.59 ms
  4. 4. vL = 0.01337 V
  5. 5. R = 9.24 kΩ
  6. 6. t = 116.8 ms

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