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
∴ ω_{0} =1 / √(LC)
= 1/ √(2 × 20 × 10^{- 6}) = 0.158 × 10^{3}
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