An RLC circuit is connected to a AC power supply. The amplitude of the power supply is 180.0V. To determine the maximum voltage across any element of the circuit one must determine the frequency at which it occurs. For the resistor, it is the resonance frequency. But what about the inductor or capacitor? Determine the maximum amplitude of the voltage across the inductor if R=90.0 ohms, C=5.4F, and L=25.0mH.

The maximum voltage across the inductor is

Explanation:

From the question we are told that

     The amplitude of the power is  

       The resistance is

        The capacitance is

        The inductance is  

According to the question the the circuit frequency is  resonance frequency

    At resonance frequency

     capacitive Reactance   is equal to the Inductive Reactance

The capacitive Reactance is mathematically represented as

Where  

     Substituting values  

So      

The inductive  Reactance is mathematically represented as

Substituting values  

The impedance of the circuit is mathematically represented as

Substituting values    

The maximum current supplied to the circuit is  

So    

=>  

Now the maximum voltage across the inductor is

So        

=>        

at right angles to each other