At resonance, what is the nature of the impedance of a series RLC circuit?

At resonance, what is the nature of the impedance of a series RLC circuit?

• A. The impedance is purely imaginary.
• B. The impedance is zero.
• C. The impedance is infinite.
• D. The impedance is purely real and equal to R.

Answer: (D)

At resonance, the inductive reactance and capacitive reactance cancel each other out because ωL equals 1/(ωC). This leaves only the resistive part, so the impedance becomes Z = R, a purely real quantity. With only resistance present, the circuit current is in phase with the applied voltage and is determined by R. The other possibilities describe a net reactance (purely imaginary), zero impedance, or infinite impedance, none of which characterize a series RLC at resonance with finite R. Therefore, the impedance is purely real and equal to R.

At resonance, the inductive reactance and capacitive reactance cancel each other out because ωL equals 1/(ωC). This leaves only the resistive part, so the impedance becomes Z = R, a purely real quantity. With only resistance present, the circuit current is in phase with the applied voltage and is determined by R. The other possibilities describe a net reactance (purely imaginary), zero impedance, or infinite impedance, none of which characterize a series RLC at resonance with finite R. Therefore, the impedance is purely real and equal to R.