# Knowledge about Serial Resonant Test System

HIMALAYAL - SHANGHAI - CHINA

In the series circuit composed of resistance, inductance and capacitance, when capacitive reactance XC is equal to inductive reactance XL, that is, XC=XL, the voltage U in the circuit has the same phase as the current I and the circuit displays pure resistance. This phenomena is called series resonance. When the circuit happens to series resonance, the circuit impedance Z = √R2 + XC - XL2 = R. The total impedance in the circuit is the minimum while the current reaches the maximum.

When the resonance occurs, because XC=XL, voltage equivalent value at inductance end and capacitance end is the same, namely, UL = UC. In addition, the phase is opposite so two voltages offset. The capacitance voltage equivalent value or the inductance is as follows: UL=UC=XLI0=ω0LIO=ω0LU/R. In the formula, ω0L/R is named as quality factor of resonance circuit, which stands for voltage ratio, that is, UL/UO or UL/U.

Quality factor is an important parameter for measuring resonance circuit characteristics. In the circuit, the bigger the reactance is and the smaller the resistance is, the higher the quality factor becomes. Hence, the voltage value on the capacitance or inductance is much larger than external applied voltage. The quality factor of common inductance and capacitance series circuit can reach ten, even hundred.

Thereby, series resonance is also called voltage resonance. In the electric power system, series resonance will generate over-voltage which is far higher than rated voltage of power grid, causing great damage to electric equipments.