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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:
XL = XC
ωL = 1 /ωC
∴ ω0 =1 / √(LC)
= 1/ √(2 × 20 × 10- 6) = 0.158 × 103
and
fo = 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
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