You want a resonance frequency of 1.09×103 Hz and already have a circuit with a 144 Ω resistor and a 24.0 mH inductor. What capacitor should be added in series to get the correct frequency?
Question
You want a resonance frequency of 1.09×103 Hz and already have a circuit with a 144 Ω resistor and a 24.0 mH inductor. What capacitor should be added in series to get the correct frequency?
Solution
The resonance frequency for a series RLC circuit is given by the formula:
f = 1 / (2π√(LC))
where: f is the frequency, L is the inductance, and C is the capacitance.
We can rearrange this formula to solve for C:
C = 1 / (4π²f²L)
Substituting the given values:
C = 1 / (4π² * (1.09×10³ Hz)² * 24.0×10⁻³ H)
After calculating the above expression, we find that the required capacitance is approximately 2.14×10⁻⁹ F or 2.14 nF.
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