Question

Calculate the value of capacity in picofarad ,
which will make 101.4 micro henry Induc-
tance to oscillate with frequency of one Mega.
hertz​

Answer 1

we have to calculate the value of capacity in pico Farad, which will make 101.4 micro Henry inductance to oscillate with frequency of 1 Mega Hertz.

solution : inductance, L = 101.4 μH = 101.4 × 10¯⁶ H

frequency of oscillation, f = 1 MHz = 10⁶ Hz

we know, resonant frequency formula, f = 1/2π√(LC)

where , C is capacitance of capacitor.

so, 10⁶ = 1/2π√(101.4 × 10¯⁶ × C)

⇒10¹² = 1/4π²(101.4 × 10¯⁶ × C)

⇒C = 1/(4π² × 101.4 × 10¯⁶ × 10¹²)

⇒C = 1/(4 × 3.14² × 101.4 × 10⁶) = 2.5 × 10¯¹⁰ F

= 250 × 10¯¹² F = 250 pF

Therefore the capacity in pico Farad is 250