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Transients (RC, RL, RLC): board exam questions with solutions

On the ECE exam under Electronics Engineering and the REE exam under Electrical Engineering Professional Subjects. Try each question before you open its solution, then practise with fresh numbers below: 2 computed question types on this topic.

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Questions

1. What is the time constant of a series RC circuit with R = 10 kΩ and C = 100 µF?

  1. 0.1 s
  2. 10 s
  3. 1.0 s
  4. 1.0 ms
Show the answer and solution

Answer: C. 1.0 s

τ = RC = 10 × 10³ × 100 × 10⁻⁶ = 1.0 s.

2. A discharged capacitor is charged from a 12 V source through a resistor. What is its voltage after two time constants?

  1. 7.58 V
  2. 10.38 V
  3. 1.62 V
  4. 11.40 V
Show the answer and solution

Answer: B. 10.38 V

v = 12(1 − e⁻²) = 12 × 0.8647 = 10.38 V.

3. A 24 V DC source is switched onto a series circuit of R = 10 Ω and L = 0.5 H. What is the current 0.1 s after switching?

  1. 2.08 A
  2. 2.40 A
  3. 0.32 A
  4. 1.52 A
Show the answer and solution

Answer: A. 2.08 A

τ = L/R = 0.05 s, final current = 24/10 = 2.4 A, i = 2.4(1 − e^(−0.1/0.05)) = 2.4(1 − e⁻²) = 2.08 A.

4. Which quantity cannot change instantaneously in a circuit with finite voltages?

  1. The voltage across an inductor
  2. The current through a capacitor
  3. The voltage across a resistor
  4. The current through an inductor
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Answer: D. The current through an inductor

Since v = L di/dt, an instantaneous jump in inductor current would require infinite voltage; so inductor current (like capacitor voltage) is continuous.

5. A 100 µF capacitor charged to 50 V discharges through a 1 kΩ resistor. How long until its voltage falls to 10 V?

  1. 80 ms
  2. 100 ms
  3. 161 ms
  4. 500 ms
Show the answer and solution

Answer: C. 161 ms

t = RC ln(V0/V) = 0.1 × ln(5) = 0.1609 s ≈ 161 ms.

6. A series RLC circuit has R = 20 Ω, L = 10 mH and C = 10 µF. How is its natural (step) response best described?

  1. Critically damped
  2. Underdamped
  3. Overdamped
  4. Undamped (sustained oscillation)
Show the answer and solution

Answer: B. Underdamped

ζ = (R/2)√(C/L) = 10√(10⁻⁵/10⁻²) = 0.316 < 1, so it is underdamped (critical R = 2√(L/C) = 63.2 Ω).

7. How much energy is stored in a 470 µF capacitor charged to 25 V?

  1. 0.147 J
  2. 0.294 J
  3. 0.0059 J
  4. 0.0118 J
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Answer: A. 0.147 J

W = ½CV² = 0.5 × 470 × 10⁻⁶ × 25² = 0.147 J.

8. For the series RLC circuit with R = 20 Ω, L = 10 mH and C = 10 µF, what is the damped natural frequency ωd?

  1. 3162 rad/s
  2. 1000 rad/s
  3. 477 rad/s
  4. 3000 rad/s
Show the answer and solution

Answer: D. 3000 rad/s

ω0 = 1/√(LC) = 3162 rad/s, α = R/(2L) = 1000 s⁻¹, ωd = √(ω0² − α²) = √(10000000 − 1000000) = 3000 rad/s.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. A discharged 4.7 µF capacitor charges from 5 V through 12 kΩ. What is its voltage 56.4 ms after the switch closes?

  1. 1 V
  2. 3.16 V
  3. 4.74 V
  4. 1.84 V
Show the answer and solution

Answer: B. 3.16 V

τ = RC = 56.4 ms; at t = 56.4 ms (1τ), v = V(1 − e^−1) = 3.16 V.

10. What is the time constant of a 50 mH inductor in series with 100 Ω?

  1. 5 s
  2. 500 µs
  3. 2 ks
  4. 2.5 ms
Show the answer and solution

Answer: B. 500 µs

τ = L/R = 50 mH/100 Ω = 500 µs.

Other topics in the same subjects

DC circuits · AC circuits · Semiconductors and diodes · BJT and FET circuits · Operational amplifiers · Oscillators and feedback · Power electronics · Digital electronics · Microprocessors and microcontrollers · Control systems · Instrumentation and measurement · Three-phase systems · Transformers · DC machines · Induction motors · Synchronous machines · Power systems and transmission · Protection: fuses, breakers, relays · Illumination · Power plant engineering · PEC: branch circuits, ampacity and protection

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