We think of the response of the circuit as the ratio of the maximum current to the maximum voltage provided. Explain why the ratio of the maximum current to the maximum current of the entire circuit will be largest when the two reactants are equal. When this is the case, we think of the RLC circuit as responding as strongly as possible to the AC current and say that it is resonating.

Z = R, i = V/Z,    w = √1 / LC

Explanation:

In an RLC circuit the impedance of the circuit is

          Z = √[R² + ()²

Where

      = wL

      X_{L} = 1 / wC

They are the reactances of the inductor and the capacitor, in this case the current advances to the voltage in the first and is delayed from the voltage in the second, so when the two values give the same reactance the current goes in phase with the voltage and the impedance is minimal

          Z = R

          V= i Z

           i = V/Z

Therefore the current is maximum, this occurs when

       w = √1 / LC

Saying that this is the resonant frequency

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