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​20 Vt = 0R = 2.2 kΩC10 µF+−vC​

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

Vs = 20 VR = 2.2 kΩC = 10 µF
τ = ms
2.Easy
+−Vs​10 Vt = 0R = 4.7 kΩC220 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage vC at t = 300 ms.

Vs = 10 VR = 4.7 kΩC = 220 µFt = 300 ms
vC = V
3.Medium
+−Vs​12 Vt = 0R = 20 ΩL47 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 = 12 VR = 20 ΩL = 47 mHt = 5 ms
vL = V
4.Medium
R = 33 Ωt = 0L68 mHi(t)

The inductor carries a steady current of 3 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 0.75 A? Find t.

i(0) = 3 AR = 33 ΩL = 68 mH
t = ms
5.Hard
+−Vs​15 Vt = 0R = 2.2 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 7.5 V, exactly 20 ms after the start. With R = 2.2 kΩ, find the capacitance C needed.

Vs = 15 VVth = 7.5 VT = 20 msR = 2.2 kΩ
C = µF
6.Hard
+−Vs​9 Vopens at t = 0R1​ = 6.8 kΩR2​ = 10 kΩi2​C10 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 = 6.8 kΩR2 = 10 kΩC = 10 µFt = 200 ms
i2 = mA

Answer key

  1. 1. τ = 22 ms
  2. 2. vC = 2.518 V
  3. 3. vL = 1.429 V
  4. 4. t = 2.857 ms
  5. 5. C = 13.12 µF
  6. 6. i2 = 0.0725 mA

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