Find the frequency at which following circuit resonates
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Given
R1 = 15 Ω
R2= 10 Ω
L1= 0.1 H
L2 = 0.2 H
C1 = 2 μF
C2 = 0.5 μF
To Find
1.Resonating frequency, F
Solution
First we need to simplify the circuit into small one.
All equipment are connected in series.
Total Inductance L = L1 + L2
= 0.1 + 0.2
= 0.3 H
Total Capacitance 1/C = 1/C1 + 1/C2
= 1/2 + 1/0.5
= 2.5
C = 0.4 μF
= 0.4 x 10^(-6) F
At resonance condition XL = XC
XL = 2 x π x F x L
XC = 1 / (2 x π x F x C)
2 x π x F x L = 1 / (2 x π x F x C)
F = 1 / ( 2 x π √ (L x C))
= 1 / (2 x π √ (0.3 x 0.4 x 10^(-6)))
F = 459.44 Hz
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