Problem
Problem
A circuit operating at Hz contains a 1 μF capacitor and a 20 Ω resistor. How large an inductor must be added in series to make the phase angle for the circuit zero? Calculate the current in the circuit if the applied voltage is 120 V.Intuitive explanation
The key insight is recognizing that a zero phase angle means the circuit is at resonance, where inductive and capacitive reactances cancel each other out. At this special frequency, the impedance is purely resistive, so voltage and current are in phase. You'll need to find the inductance that makes , then use Ohm's law with the now-purely-resistive impedance to find the current.
Intuitive explanation
The key insight is recognizing that a zero phase angle means the circuit is at resonance, where inductive and capacitive reactances cancel each other out. At this special frequency, the impedance is purely resistive, so voltage and current are in phase. You'll need to find the inductance that makes , then use Ohm's law with the now-purely-resistive impedance to find the current.