Question

Resonance condition of a series lcr-circuit. Calculate its resonant frequency

Answer 1

RLC circuit consists of a inductor , resistor , and capacitor in series with an ac source .

In a series RLC circuit , there comes a frequency of ac source when the inductive reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor .

We can say that XL = XC

where, XL = inductive reactance of inductor

           XC = capacitive reactance of the capacitor

This point is called the Resonant Frequency point .

As, XL = 2pi * f * L

XC = 1/(2pi * f * C)

where, f = frequency of ac source

           C  =  capacitance

            L = inductance

 When  XL = XC

=>  2pi * f * L =  1/(2pi * f * C)

=>  f² = 1/(2pi *L * 2pi *C)

=>  f² = 1/(4π²LC)

=>  f  =  √1/(4π²LC)

=>  f  =  1/(2π√LC)    Hz

Thus, resonant frequency of lcr circuit  =   1/(2π√LC)    Hz