DC and AC Circuit Analysis Flashcards

What is the bandwidth of a series RLC resonant circuit with f₀ = 1000 Hz and Q = 50?

Answer: 20 Hz

Bandwidth BW = f₀/Q = 1000/50 = 20 Hz, representing the range of frequencies within 3 dB of the resonant peak.

In an AC circuit, the complex power S is defined as:

Answer: S = V × I* (voltage times conjugate of current)

Complex power S = V_rms × I*_rms gives the full power triangle: S = P + jQ, where P is real power and Q is reactive power.

When analyzing a circuit using Norton's theorem, what is the Norton current (IN)?

Answer: The short-circuit current at the output terminals

Norton current IN is found by short-circuiting the output terminals and calculating the resulting current through that short.

In phasor notation, multiplying a phasor by j (the imaginary unit) results in:

Answer: A 90° phase lead

Multiplying by j = 1∠90° rotates a phasor counterclockwise by 90°, corresponding to a 90° phase advance (lead).

The impedance of a series circuit with R = 3 Ω, XL = 6 Ω, and XC = 2 Ω is:

Answer: 5 Ω at 53.13°

Z = R + j(XL - XC) = 3 + j4, so |Z| = √(9+16) = 5 Ω and θ = arctan(4/3) ≈ 53.13°.

What does Millman's theorem allow engineers to calculate directly?

Answer: The common voltage across parallel branches with different sources

Millman's theorem provides a direct formula for the voltage at a node where multiple branches (each with a source and impedance) connect in parallel.

In a purely capacitive AC circuit, which statement correctly describes current and voltage?

Answer: Current leads voltage by 90°

In a pure capacitor, the current leads the voltage by 90° because current flows as the capacitor charges before the voltage across it fully develops.