Physics
Physics
Problem
Consider a series circuit containing a resistor R, an inductor L and a capacitor C connected to an a.c. source of emf. Explain, with suitable reasoning, why the average power consumed in the circuit is maximum and the power factor becomes unity at the condition of electrical resonance. a. (a) State the condition for electrical resonance in a series RLC circuit. b. (b) Using relevant circuit relations, explain why the power factor equals unity at resonance. c. (c) Hence justify why the average power transferred to the circuit attains its maximum value at resonance.Intuitive explanation
At resonance, the inductive and capacitive reactances cancel each other out——leaving only resistance to oppose current flow. This means the impedance is minimized to just , allowing maximum current to surge through the circuit. Since power dissipation depends on both current and the alignment between voltage and current (the power factor), resonance achieves both: peak current and perfect phase alignment where voltage and current oscillate together. The power factor becomes unity because there's no net reactance to create a phase lag, so all the source's energy goes into heating the resistor rather than sloshing back and forth between the inductor and capacitor.
Intuitive explanation
At resonance, the inductive and capacitive reactances cancel each other out——leaving only resistance to oppose current flow. This means the impedance is minimized to just , allowing maximum current to surge through the circuit. Since power dissipation depends on both current and the alignment between voltage and current (the power factor), resonance achieves both: peak current and perfect phase alignment where voltage and current oscillate together. The power factor becomes unity because there's no net reactance to create a phase lag, so all the source's energy goes into heating the resistor rather than sloshing back and forth between the inductor and capacitor.