89.MET February 2020 Q.8(b)

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