Series Resonance

In a series RLC circuit there becomes a frequency point were the inductive reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor. In other words, X_L = X_C. The point at which this occurs is called the Resonant Frequency point, ( ƒ_r ) and as we are analysing a series RLC circuit this resonance frequency produces a Series Resonance circuit.

As the frequency approaches infinity the inductors reactance would also increase towards infinity with the circuit element acting like an open circuit. However, as the frequency approaches zero or DC, the inductors reactance would decrease to zero, causing the opposite effect acting like a short circuit. This means then that inductive reactance is "Proportional" to frequency and is small at low frequencies and high at higher frequencies.

The major difference between series and parallel resonance is that due to the formation of Tank Circuit , large amount of circulating current exists and it will be exactly oppositely following series resonance current curve.   

As the frequency approaches infinity the capacitors reactance would reduce to zero causing the circuit element to act like a perfect conductor of 0Ω's. However, as the frequency approaches zero or DC level, the capacitors reactance would rapidly increase up to infinity causing it to act like a very large resistance acting like an open circuit condition. This means then that capacitive reactance is "Inversely proportional" to frequency for any given value of capacitance.

Electrical resonance occurs in an AC circuit when the two reactances which are opposite and equal cancel each other out as X_L = X_C and the point on the graph at which this happens is were the two reactance curves cross each other. 

Note that when the capacitive reactance dominates the circuit the impedance curve has a hyperbolic shape to itself, but when the inductive reactance dominates the circuit the curve is non-symmetrical due to the linear response of X_L. If the circuits impedance is at its minimum at resonance then consequently, the circuits  admittance must be at its maximum and one of the characteristics of a series resonance circuit is that admittance is very high. But this can be a bad thing because a very low value of resistance at resonance means that the circuits current may be dangerously high.

The frequency response curve of a series resonance circuit shows that the magnitude of the current is a function of frequency and plotting this onto a graph shows us that the response starts at near to zero, reaches maximum value at the resonance frequency when I_MAX = I_R and then drops again to nearly zero as ƒ becomes infinite. The result of this is that the magnitudes of the voltages across the inductor, L and the capacitor, C can become many times larger than the supply voltage, even at resonance but as they are equal and at opposition they cancel each other out. As a series resonance circuit only functions on resonant frequency, this type of circuit is also known as an Acceptor Circuit because at resonance, the impedance of the circuit is at its minimum so easily accepts the current whose frequency is equal to its resonant frequency. The effect of resonance in a series circuit is also called "voltage resonance"