The antenna current of an AM transmitter is 8A when only the...

The power dissipated in any circuit is a function of the square of voltage across the circuit and the effective resistance of the circuit. Equation of AM wave reveals that it has three components of amplitude Clearly; power output must be distributed among these components.

Carrier power, ${P}_{c} = \dfrac{{\left({E}_{c} / \sqrt{2}\right)}^{2}}{R} = \dfrac{{E}_c^{2}}{2R}$

Total power of side bands,

${P}_{S} = \dfrac{{\left(m{E}_{c} / 2\sqrt{2}\right)}^{2}}{R} + \dfrac{{\left(m{E}_{c} / 2\sqrt{2}\right)}^{2}}{R} = \dfrac{m^{2}{E}_c^{2}}{4R}$

$∴ \dfrac{{P}_{S}}{{P}_{C}} = \dfrac{1}{2}m^{2}$

and ${P}_{T} = {P}_{C} + {P}_{S} = {P}_{C} \left(1 + \dfrac{m^{2}}{2}\right)<br /><br />$∴ $\dfrac{{P}_{T}}{{P}_{C}} =1 + \dfrac{m^{2}}{2}$⇒ {\left(\dfrac{{I}_{T}}{{I}_{C}}\right)}^{2} = 1 +\dfrac{m^{2}}{2}

Given that, ${I}_{T} = 8.93A, {I}_{C} = 8A, m = ?$

$∴ {\left(\dfrac{8.93}{8}\right)}$^{2} = 1 + $\dfrac{m^{2}}{2}<br /><br />Or 1.246 = 1 + \dfrac{m^{2}}{2}$ or$\dfrac{m^{2}}{2} =0.246$

Or $m = \sqrt{2 \times 0.246} =0.701 = 70.1$