DC Circuit Analysis & Theory Flashcards

A 100 μF capacitor is connected in series with a 10 kΩ resistor and a 50 V DC source. What is the time constant (τ) of the circuit?

Answer: 1 s

τ = RC = 10,000 × 100×10⁻⁶ = 1 s.

After one time constant (τ), a charging capacitor reaches approximately what percentage of the supply voltage?

Answer: 63%

V(τ) = V_s(1 − e⁻¹) ≈ 0.632 × V_s, so approximately 63%.

In a fully charged capacitor in a DC steady-state circuit, what current flows through it?

Answer: Zero

At steady state, the capacitor voltage equals the source voltage and no current flows (capacitor acts as an open circuit).

Which of the following correctly describes the energy stored in a capacitor?

Answer: E = ½CV²

The energy stored in a capacitor is E = ½CV², where C is capacitance and V is voltage across it.

Two capacitors of 4 μF and 6 μF are connected in series. What is the equivalent capacitance?

Answer: 2.4 μF

1/C = 1/4 + 1/6 = 5/12; C = 12/5 = 2.4 μF.

A 50 μF capacitor charges through a 20 kΩ resistor from a 100 V source. Approximately how long does it take to reach 99% of the supply voltage?

Answer: 5 s

τ = 20,000 × 50×10⁻⁶ = 1 s; 99% is reached at ≈ 5τ = 5 s.

In an RC discharging circuit, the voltage across the capacitor after two time constants is approximately:

Answer: 13.5% of initial

V = V₀ × e^(−2) ≈ 0.135 × V₀, so about 13.5% of the initial voltage remains.