The tuned circuit of the oscillator in a simple AM transmitter employs $40 μ H$ coil and 12 nano-farad (nF) capacitor. If the oscillator output is modulated by audio frequency of 5 kHz, which of the following frequencies doesn’t appear in the output AM?

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$f_{L S B} = 225 k H z$

$f_{U S B} = 235 k H z$

$f_{c} = 230 k H z$

$f_{c} = 235 k H z$

answer is D.

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Detailed Solution

$G i v e n : L = 40 \times 10^{- 6} H, C = 12 \times 10^{- 9} F, f_{m} = 5 k H z C a r r i e r f r e q u e n c y, f_{c} = \frac{1}{2 π \sqrt{L C}} \Rightarrow f_{c} = \frac{1}{2 \times 3.14 \sqrt{480 \times 10^{- 15}}} \Rightarrow f_{c} = \frac{1}{6.28 \sqrt{48 \times 10^{- 14}}} \Rightarrow f_{c} = \frac{10^{7}}{6.28 \times 6.9} = \frac{10000}{43.332} \times 10^{3} ≃ 230 k H z f_{U S B} = f_{m} + f_{c} = 230 + 5 = 235 K H z f_{L S B} = f_{m} - f_{c} = 230 - 5 = 225 K H z$