What is the capacitance of the capacitor required if an LC oscillator that uses an inductance of L = 15mH to produce a sine wave of frequency 100kHz ?
Question
What is the capacitance of the capacitor required if an LC oscillator that uses an inductance of L = 15mH to produce a sine wave of frequency 100kHz ?
Solution 1
The frequency of an LC oscillator 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 * (100kHz)² * 15mH) C = 1 / (4 * (3.14159)² * (100 * 10^3 Hz)² * 15 * 10^-3 H)
After calculating the above expression, we get:
C ≈ 1.06 * 10^-12 F
So, the capacitance of the capacitor required is approximately 1.06 picofarads (pF).
Solution 2
The frequency of an LC oscillator 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 * (100kHz)² * 15mH) C = 1 / (4 * (3.14159)² * (100 * 10^3 Hz)² * 15 * 10^-3 H)
After calculating the above expression, we get:
C ≈ 1.06 * 10^-12 F
So, the capacitance of the capacitor required is approximately 1.06 picofarads (pF).
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