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(B) The condition for proper detection of an amplitude modulated signal without distortion is that the time constant $	au = RC$ must satisfy the rela

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$10.61\, kHz$

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(B) The condition for proper detection of an amplitude modulated signal without distortion is that the time constant $	au = RC$ must satisfy the relation $	au \le \frac{1}{\omega_m m_a}$,where $\omega_m = 2\pi f_m$ is the angular frequency of the modulating signal and $m_a$ is the modulation index.Given:$R = 100\, k\Omega = 10^5\, \Omega$$C = 250\, pF = 250 	imes 10^{-12}\, F$$m_a = 60\% = 0.6$The maximum frequency $f_m$ that can be detected is given by:$f_m = \frac{1}{2\pi m_a RC}$Calculating the time constant:$	au = RC = 10^5 	imes 250 	imes 10^{-12} = 2.5 	imes 10^{-5}\, s$Substituting the values:$f_m = \frac{1}{2 	imes 3.1416 	imes 0.6 	imes 2.5 	imes 10^{-5}}$$f_m = \frac{1}{9.4248 	imes 10^{-5}}$$f_m \approx 10610\, Hz = 10.61\, kHz$

$A$ diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity $250\, pF$ in parallel with a load resistance $100\, k\Omega$. Find the maximum modulated frequency which could be detected by it.

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