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

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage v_C at t = 75 ms.

V_s = 6 VR = 6.8 kΩC = 22 µFt = 75 ms

v_C = V

2.Easy

The capacitor is uncharged when the switch closes at t = 0. Find the capacitor voltage v_C at t = 20 ms.

V_s = 24 VR = 1 kΩC = 47 µFt = 20 ms

v_C = V

3.Medium

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.

V_s = 9 VR₁ = 10 kΩR₂ = 2.2 kΩC = 33 µF

τ = ms

4.Medium

The inductor carries no current before the switch closes at t = 0. Find the current i at t = 15 ms.

V_s = 12 VR = 22 ΩL = 150 mHt = 15 ms

i = A

5.Hard

A timer starts charging an uncharged capacitor through a resistor from a 5 V supply at t = 0. It must trigger when the capacitor voltage reaches 4.5 V, exactly 1000 ms after the start. With C = 22 µF, find the resistance R needed.

V_s = 5 VV_th = 4.5 VT = 1000 msC = 22 µF

R = kΩ

6.Hard

The switch has been closed for a long time, so the circuit is in steady state. At t = 0 the switch opens. Find the capacitor voltage v_C at t = 250 ms.

V_s = 12 VR₁ = 2.2 kΩR₂ = 4.7 kΩC = 33 µFt = 250 ms

v_C = V

Answer key

1. v_C = 2.366 V
2. v_C = 8.318 V
3. τ = 59.51 ms
4. i = 0.485 A
5. R = 19.74 kΩ
6. v_C = 1.631 V

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