In a series RLC circuit, at resonance the impedance is approximately equal to

In a series RLC circuit, at resonance the impedance is approximately equal to

• A. R
• B. ∞
• C. 0
• D. ωL

Answer: (A)

At resonance the inductive and capacitive reactances cancel because ωL = 1/(ωC). The total impedance of a series RLC is Z = R + j(ωL − 1/(ωC)). When the reactive part cancels, Z = R, so the circuit looks purely resistive and the impedance equals the resistance. This is also why the current is maximized for a given applied voltage, since I = V/R. The other possibilities would require a net reactive part (∞ or 0 would mean no current flow or a perfect short, which isn’t the case at resonance), but at resonance the reactive part vanishes and only the resistance remains.

At resonance the inductive and capacitive reactances cancel because ωL = 1/(ωC). The total impedance of a series RLC is Z = R + j(ωL − 1/(ωC)). When the reactive part cancels, Z = R, so the circuit looks purely resistive and the impedance equals the resistance. This is also why the current is maximized for a given applied voltage, since I = V/R. The other possibilities would require a net reactive part (∞ or 0 would mean no current flow or a perfect short, which isn’t the case at resonance), but at resonance the reactive part vanishes and only the resistance remains.