Question

The capacitance in a series RCL circuit is C₁ = 3.7 μF, and the corresponding resonant frequency is f₀₁ = 5.1 kHz. The generator frequency is 2.9 kHz. What is the value of the capacitance C₂ that should be added to the circuit so that the circuit will have a resonant frequency that matches the generator frequency?

Answer 1

use,
2*3.14*fo1 = (1/(L*C1))^1/2
2*3.14*5.1 = (1/(L*3.7))^1/2

let affter adding C final capacitance become C3
so,
2*3.14*fo2 = (1/(L*C))^1/2
2*3.14*2.9 = (1/(L*C))^1/2

divide first equation by 2
5.1/2.9 = (C/3.7)^1/2
1.76 = (C/3.7)^1/2
C/3.7 = 3.1
C = 3.1*3.7
= 11.5 uF

since,
C > C1
so, C2 must be added in parral to C1
so,
C = C1 + C2
11.5 = 3.7 + C2
C2 = 7.8 uF

Answer: 7.8 uF