AC voltage applied to a LCR Circuit

What is the voltage equation for an LCR circuit according to Kirchhoff's law?

• L di/dt + qR + i/C = v

• L di/dt + iR + q/C = v

• L di/dt + iR + qC = v

• L dq/dt + iR + q/C = v

In a phasor diagram, how does the voltage across a capacitor relate to the current phasor?

• It lags the current phasor by π/2

• It is opposite to the current phasor

• It leads the current phasor by π/2

• It is in phase with the current phasor

What is the expression for impedance (Z) in an LCR circuit?

• Z = √(R² + XC² + XL²)

• Z = R² + XC² + XL²

• Z = √(R² + (XC - XL)²)

• Z = R + XC + XL

Which method provides a steady-state solution for the LCR circuit?

• Phasor diagram method

• Graphical method

• Analytical method

• Numerical method

What is the resonant frequency (ω₀) in an RLC circuit?

• ω₀ = 1/√(LC)

• ω₀ = √(LC)

• ω₀ = C/L

• ω₀ = L/C

At resonance, what is the relationship between capacitive reactance (XC) and inductive reactance (XL)?

• XC = XL

• XC ≠ XL

• XC > XL

• XC < XL

What is the maximum amplitude of current at resonant frequency in an RLC circuit?

• im = vm/(R + Z)

• im = vm/(XC + XL)

• im = vm/R

• im = vm/Z

What does the quality factor (Q) of a circuit indicate?

• The sharpness of resonance

• The total capacitance of the circuit

• The total resistance of the circuit

• The total inductance of the circuit

How is the sharpness of resonance related to the bandwidth of the circuit?

• Sharpness is inversely proportional to bandwidth

• Sharpness is directly proportional to bandwidth

• Sharpness is equal to bandwidth

• Sharpness is unrelated to bandwidth

What is the formula for the quality factor (Q) in terms of ω₀, L, and R?

• Q = ω₀L/R

• Q = L/ω₀R

• Q = ω₀R/L

• Q = R/ω₀L