Electrical Circuits Flashcards

The transfer function H(s) = V_out(s)/V_in(s) of a simple RC low-pass filter (R in series, C to ground) is:

Answer: 1/(1+sRC)

V_out = V_in × (1/sC)/(R + 1/sC) = V_in/(1 + sRC), giving H(s) = 1/(1+sRC).

The bandwidth of a series RLC circuit with resonant frequency ω₀ = 5000 rad/s and Q = 25 is:

Answer: 200 rad/s

Bandwidth BW = ω₀/Q = 5000/25 = 200 rad/s.

In AC circuit analysis, the apparent power S is related to real power P and reactive power Q by:

Answer: |S|² = P² + Q²

The power triangle gives |S|² = P² + Q², where S is in VA, P in W, and Q in VAR.

A 10 Ω resistor and a 10 Ω inductive reactance are connected in parallel. What is the magnitude of the equivalent impedance?

Answer: 7.07 Ω

Z_eq = (10 × j10)/(10 + j10) = j100/(10+j10); |Z_eq| = 100/|10+j10| = 100/(10√2) = 10/√2 ≈ 7.07 Ω.

Kirchhoff's Voltage Law (KVL) is a consequence of:

Answer: Conservation of energy

KVL states that the algebraic sum of voltages around any closed loop is zero, which follows from conservation of energy (work done around a closed path is zero).

For an ideal transformer with turns ratio n = N₁/N₂ = 4, if the secondary voltage is 30 V, the primary voltage is:

Answer: 120 V

V₁/V₂ = N₁/N₂ = n, so V₁ = n × V₂ = 4 × 30 = 120 V.

The Fourier series of a periodic waveform represents it as a sum of:

Answer: Sinusoids at the fundamental frequency and its harmonics

The Fourier series decomposes a periodic signal into DC plus sinusoidal components at the fundamental frequency and integer multiples (harmonics).