Question

A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 μH, what must be the range of its variable capacitor?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]

Answer 1

The range of frequency (ν) of a radio is 800 kHz to 1200 kHz.

Lower tuning frequency, ν₁ = 800 kHz = 800 × 10³ Hz

Upper tuning frequency, ν₂ = 1200 kHz = 1200× 10³ Hz

Effective inductance of circuit L = 200 μH = 200 × 10⁻⁶ H

Capacitance of variable capacitor for ν₁ is given as_:

C₁

Where,

ω₁ = Angular frequency for capacitor C₁

Capacitance of variable capacitor for ν_2,

C₂

Where,

ω₂ = Angular frequency for capacitor C₂

Hence, the range of the variable capacitor is from 88.04 pF to 198.1 pF.