Q. 103.6( 16 Votes )

# 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?

Answer :

Given: frequency range of radio waves = 800 kHz to 1200 kHz

Therefore, low tuning frequency of radio wave v_{1} = 800 kHz, or 800 × 10^{-3} Hz

Upper tuning frequency v_{2} = 1200 kHz or 1200 × 10^{-3} Hz

Inductance L = 200 μH or 200 × 10^{-6}H

Capacitance of the variable capacitor for low tuning frequency v_{1} is given by the following relation:

C_{1} = 1/ ω_{1}^{2}L……………..(i)

Where ω is equal to 2πv_{1}

Substituting in equation (i), we get

C_{1} = 1/{(2π × 800 × 10^{-3}Hz)^{2} × 200 × 10^{-6}H}

On calculating we get

C_{1} = 1.9809 × 10^{-10}F

Or C_{1} = 198.1 pF

Capacitance of the variable capacitor for upper tuning frequency v_{2} is given by the following relation:

C_{2} = 1/ ω_{2}^{2}L……………..(ii)

Where ω is equal to 2πv_{2}

Substituting in equation (i), we get

C_{2} = 1/{(2π × 1200 × 10^{-3}Hz)^{2} × 200 × 10^{-6}H}

On calculating we get

⇒ C_{2} = 88.04 pF

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

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