Find the resonant frequency:

Find the resonant frequency ω0 (or f0) for the given series RLC circuit

v = Vm sin ωt = 50 sin ωt

Figure

Also determine the expression for resonant current.

Solution

R = 10 Ω, L = 2 Henry, C = 20 μF

 Under resonance:

                                  X_L = X_C

                               ωL =   1 /ωC

∴          ω₀ =1 / √(LC)

=          1/ √(2 × 20 × 10^{- 6})     = 0.158 × 10³

and

           f_o   = 1/2π √( LC)  = 25.16 Hz

Current i is given by i = V/ Z

But at resonance Z = R or 10 Ω

So        i = Vm sin ωt/R    =50 sin ωt/10      = 5 sin ωt Amp