Question

The antenna current of an AM transmitter is $8A$ when only the carrier is sent, but it increases to $8.93A$ when the carrier is modulated by a single wave. The percentage modulation is

• A. $60.1\%$
• B. $70.1\%$
• C. $80.1\%$
• D. $50.1\%$

Answer 1

The correct option is B $70.1\%$

$P_S=\frac{1}{2}{m}^2{P}_C$
$P_T=P_C+P_S=P_C(1+\frac{m^2}{2})$
$\frac{P_T}{P_C}=1+\frac{m^2}{2}$
$(\frac{I_T}{I_C}{)}^2=1+\frac{m^2}{2}$

Given that $I_T=8.93A,I_C=8A,$ we have
$(\frac{8.93}{8}{)}^2=1+\frac{m^2}{2}$
$1.246=1+\frac{m^2}{2}$
$\frac{m^2}{2}=0.246$
$m=\sqrt{2\times 0.246}=0.701=70.1\%$