**Voltage Magnification in Series Resonance:**

Voltage Magnification in Series Resonance – If we assume that the voltage applied to the series RLC circuit is V, and the current at resonance is I, then the voltage across L is **V _{L} = IX_{L} = (V/R) ω_{r}L.**

Similarly, the voltage across C

Since ,

where ω_{r} is the frequency at resonance.

Therefore

The ratio of voltage across either L or C to the voltage applied at resonance can be defined as magnification.

**The Quality Factor (Q) and its Effect on Bandwidth:**

The quality factor, Q, is the ratio of the reactive power in the inductor or capacitor to the true power in the resistance in series with the coil or capacitor.

The quality factor

In an inductor, the max energy stored is given by **LI ^{2}/2**

Quality factor of the coil

Similarly, in a capacitor, the max energy stored is given by **CV ^{2}/2**

The energy dissipated per cycle **= (I/√2) ^{2} R x T**

The quality factor of the capacitance circuit

In series circuits, the quality factor

We have already discussed the relation between bandwidth and quality factor, which is

A higher value of circuit Q results in a smaller bandwidth. A lower value of Q causes a larger bandwidth.