The formula for finding w in this scenario is w = 1/√(LC), where L is the inductance of the circuit and C is the capacitance.
The inductance and capacitance values can be determined by measuring the physical properties of the circuit components, such as the number of turns in the inductor or the size of the capacitor. They can also be calculated using equations based on the circuit's geometry and materials.
When the EMF (electromotive force) is in phase with the current, it means that the voltage and current are reaching their maximum and minimum values at the same time. This indicates that the circuit is in resonance, with the energy being transferred back and forth between the inductor and capacitor without any energy loss.
Changing the inductance or capacitance in an AC RLC circuit will affect the value of w, as it is directly proportional to the square root of the product of these two values. Increasing the inductance or capacitance will result in a decrease in w, while decreasing either value will result in an increase in w.
Finding w in this scenario allows us to determine the resonant frequency of the circuit, which is the frequency at which the circuit is most efficient and has the highest amplitude of current. This can be useful in designing and optimizing electronic circuits for specific purposes.