# 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.

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