If \(E_c\) and \(E_m\) are peak values of carrier and modulating signals, respectively then for \(100 \%\)…
If \(E_c\) and \(E_m\) are peak values of carrier and modulating signals, respectively then for \(100 \%\) modulation,
\(E_c=\frac{E_m}{2}\)
\(\frac{E_c^2}{2}=E_m^2\)
\(E_{\mathrm{c}}=E_m\)
\(E_c=2 E_m\)
Solution
Key idea Modulation index of a modulated signal is
\(\mu=\frac{E_m}{E_c}\)
Where, \(E_m\) and \(E_c\) are peak values of modulating signal and carrier signal.
For \(100 \%\) modulation, modulation index should be unity.
Hence, \(\mu=1=\frac{E_m}{E_c}\)
\(\Rightarrow \quad E_m=E_c\)
\(\therefore\) The correct option is (c).