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7.10 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 radio wave.]

0 4 Views | Posted 4 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

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

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

    Effective inductance of the circuit, L = 200 μH = 200 ×10-6 H

    Capacitance of variable capacitor for lower tuning frequency ( ν1) is given as

    C1 = 1ω12L , where ω1 is the angular frequency for capacitor C1 = 2 πν1

    Hence, ω1 = 2 π× 800 ×103 = 5.026 ×106 rad/s

    C1 = 1ω12L = 1(5.026×106)2×200×10-6 F = 1.9789 ×10-12 F = 197.89 pF

    Capacitance of variable capacitor for lower tuning frequency ( ν2) is given as

    C2 = 1ω22L , where ω2&

    ...more

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