Let an alternating emf E = E0 sin or be applied across it. Let 'i' is the current flowing through it.
VL = iXL , VC = iXC , VR = iR
E2 = VR2 + (VL - VC)2
E2 = i2 [R2 + (XL - XC)2]
∴ \(i=\frac{E}{\sqrt{R^2+(X_L-X_C)^2}}\)
Where \(\sqrt{R^2+(X_L-X_C)^2}=Z\)
\(tan\,\phi =\frac{X_L-X_C}{R}\)
When \(\omega L=\frac{1}{\omega C}\)
We have Z = R
Hence current will be maximum. This is the case of resonance.
\(\omega L=\frac{1}{\omega C}\)
\(\omega ^ 2=\frac{1}{LC}\)
∴ \(\omega =\frac{1}{\sqrt{LC}}\)
\(2\pi f_0 =\frac{1}{\sqrt{LC}}\)
\(f_0=\frac{1}{2\pi\sqrt{LC}}\)
where f0 is the resonant frequency.
