Physics - Current Electricity Question with Solution | TestHub

The rms value of carrier current is ${\mathrm{I}}_{\mathrm{c}}=8\mathrm{A}$. The rms value of modulated current $=I_c+I_m=8.93\mathrm{A}={\mathrm{I}}_{\mathrm{t}}$ Percentage modulation $={\mathrm{m}}_{\mathrm{a}}\times 100$ The current relation in AM wave is $\frac{{\mathrm{I}}_{\mathrm{t}}^2}{{\mathrm{I}}_{\mathrm{c}}^2}=1+\frac{{\mathrm{m}}_{\mathrm{a}}^2}{2}\Rightarrow {\mathrm{m}}_{\mathrm{a}}=\sqrt{(\frac{{\mathrm{I}}_{\mathrm{t}}^2}{{\mathrm{I}}_{\mathrm{c}}^2-1)2}}$ $\Rightarrow$ Modulation index, ${\mathrm{m}}_{\mathrm{a}}=\sqrt{\left(\frac{(8.93{)}^2}{8^2}-1\right)2}$ $\begin{array}{rl}=\sqrt{\left(\frac{79.7}{64}-1\right)2}& =\sqrt{(1.24-1)2}\\ & =0.701\\ \text{ Percentage modulation }& ={\mathrm{m}}_{\mathrm{a}}\times 100=70.1\%\end{array}$