For the output of an $AM$ detector circuit to follow the envelope of the carrier wave,which condition must be satisfied? ($T_c$ is the time period of the carrier wave.)

If a carrier wave $C(t) = A \sin \omega_c t$ is amplitude modulated by a modulating signal $m(t) = A \sin \omega_m t$,then the equation of the modulated signal $[C_m(t)]$ and its modulation index are respectively:

The characteristic impedance of a coaxial cable is typically in the range of ..........

For an amplitude modulated wave,the modulation index is found to be $0.5$. If the maximum amplitude is found to be $10.0 \ V$,then the minimum amplitude is: (in $V$)

If the ratio of the maximum and minimum amplitudes of an amplitude modulated wave is $7:3$,then the modulation index is

$A$ telephonic communication service is working at a carrier frequency of $20 GHz$. Only $20 \%$ of it is utilized for transmission. If each channel requires a bandwidth of $5 kHz$,then the number of telephonic channels that can be transmitted simultaneously are