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 = 6.8 kΩC33 µF+−vC​

The capacitor is uncharged when the switch closes at t = 0. How long after the switch closes does the capacitor voltage reach 80% of its final value? Find t.

Vs = 6 VR = 6.8 kΩC = 33 µF
t = ms
2.Easy
+−Vs​15 Vt = 0R = 1 kΩC10 µF+−vC​

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

Vs = 15 VR = 1 kΩC = 10 µF
τ = ms
3.Medium
+−Vs​10 Vt = 0R = 68 ΩL33 mHi(t)

The inductor carries no current before the switch closes at t = 0. Find the current i at t = 1 ms.

Vs = 10 VR = 68 ΩL = 33 mHt = 1 ms
i = A
4.Medium
+−Vs​12 Vt = 0R = 68 ΩL10 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 = 12 VR = 68 ΩL = 10 mH
t = ms
5.Hard
+−Vs​20 Vopens at t = 0R1​ = 1 kΩR2​ = 2.2 kΩi2​C22 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 = 25 ms.

Vs = 20 VR1 = 1 kΩR2 = 2.2 kΩC = 22 µFt = 25 ms
i2 = mA
6.Hard
+−Vs​24 VR1​ = 33 ΩR2​ = 47 Ωopens at t = 0L68 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 = 33 ΩR2 = 47 ΩL = 68 mHt = 1 ms
i = A

Answer key

  1. 1. t = 361.2 ms
  2. 2. τ = 10 ms
  3. 3. i = 0.1283 A
  4. 4. t = 0.1019 ms
  5. 5. i2 = 3.729 mA
  6. 6. i = 0.4318 A

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