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Question
A radio can tune over the frequency range of a portion of the MW broadcast band (800kHz -1200kHz). If its LC circuit has an effective inductance of 200mH, what must be the range of its variable condenser?
Solution
Given:
f1 = 800 kHz = 0.8 × 106 Hz
f2 = 1200 kHz = 1.2 × 106 Hz
L = 200 mH = 200 × 10-3 = 0.2 H
To find: Range of condenser
Formula: f = `1/(2pisqrt"LC")`
Calculation:
- For f1 = 0.8 × 106 Hz:
From formula,
C1 = `1/(4pi^2"f"^2"L")`
= `1/(4 xx 3.142^2 xx (0.8 xx 10^6)^2 xx 0.2)`
≈ 198 × 10-15 F
≈ 198 pF - For f2 = 1.2 × 106 Hz:
From formula,
C2 = `1/(4pi^2"f"^2"L")`
= `1/(4 xx 3.142^2 xx (1.2 xx 10^6)^2 xx 0.2)`
≈ `88 xx 10^-15` F
≈ 88 pF
The range of the variable condenser is 88 pF to 198 pF.
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