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?
Given: frequency range of radio waves = 800 kHz to 1200 kHz
Therefore, low tuning frequency of radio wave v1 = 800 kHz, or 800 × 10-3 Hz
Upper tuning frequency v2 = 1200 kHz or 1200 × 10-3 Hz
Inductance L = 200 μH or 200 × 10-6H
Capacitance of the variable capacitor for low tuning frequency v1 is given by the following relation:
C1 = 1/ ω12L……………..(i)
Where ω is equal to 2πv1
Substituting in equation (i), we get
C1 = 1/{(2π × 800 × 10-3Hz)2 × 200 × 10-6H}
On calculating we get
C1 = 1.9809 × 10-10F
Or C1 = 198.1 pF
Capacitance of the variable capacitor for upper tuning frequency v2 is given by the following relation:
C2 = 1/ ω22L……………..(ii)
Where ω is equal to 2πv2
Substituting in equation (i), we get
C2 = 1/{(2π × 1200 × 10-3Hz)2 × 200 × 10-6H}
On calculating we get
⇒ C2 = 88.04 pF
Therefore, the range of its variable capacitor is from 88.04 pF to 198.1 pF.