Answer :
The capacitance for the LC circuit with a frequency of 98.3 MHz FM station and an inductance of 2.8 µH is approximately 1.898 pF.
To determine the required capacitance value for an LC circuit that resonates at a specific frequency, we use the resonant frequency formula:
Formula:
f = 1 / (2π√(L × C))
Where:
f is the resonant frequency in hertz (Hz)L is the inductance in henries (H)C is the capacitance in farads (F)
Step-by-step Solution:
- Convert the units for inductance and frequency:
Inductance (L): 2.8 µH = 2.8 x 10⁻⁶ H.
Frequency (f): 98.3 MHz = 98.3 x 10⁶ Hz
- Rearrange the resonant frequency formula to solve for capacitance (C):
C= 1/[4π²f²L]
- Plug in the values:
C = 1 / [ 4 × (π²) × (98.3 x 10⁶)²× (2.8 x 10⁻⁶) ].
C ≈ 1 / [ 4 × 9.8696 × 9.65689 × 10¹⁵ × 2.8 × 10⁻⁶ ].
C ≈ 1.898 x 10⁻¹²F.
