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 current i(0⁺) just after the switch closes.

V_s = 24 VR = 6.8 kΩC = 220 µF

i(0⁺) = mA

2.Easy

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

V_s = 10 VR = 3.3 kΩC = 10 µFt = 75 ms

v_C = V

3.Medium

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. How long does it take for the current to fall to 0.5 A? Find t.

i(0) = 2 AR = 15 ΩL = 220 mH

t = ms

4.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 capacitor voltage v_C at t = 100 ms.

V_s = 6 VR₁ = 1 kΩR₂ = 4.7 kΩC = 47 µFt = 100 ms

v_C = V

5.Hard

Just before the switch closes at t = 0, the capacitor holds 30 V with the polarity shown. How long does it take for v_C to reach 15.6 V? Find t.

V_s = 12 VR = 10 kΩC = 10 µFv_C(0) = 30 V

t = ms

6.Hard

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 0.96 A? Find t.

V_s = 24 VR₁ = 20 ΩR₂ = 20 ΩL = 68 mH

t = ms

Answer key

1. i(0⁺) = 3.529 mA
2. v_C = 8.97 V
3. t = 20.33 ms
4. v_C = 4.573 V
5. t = 160.9 ms
6. t = 3.115 ms

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