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# Calculate the power developed by an amplitude modulated wave in a load resistance of 100Ω, if the peak voltage of the carrier wave is 100V and the modulation index is 0.4.A) 50 wattB) 54 wattC) 104 wattD) 4 watt

Last updated date: 13th Jun 2024
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Hint: Amplitude modulation is a technique that is used in electronic communication, mainly for transmitting a message with a radio carrier wave. In this, the amplitude of the carrier wave is varied in proportion to the message signal.

Complete step by step solution:
Given data:
Load resistance, R $=$100 ohms
Voltage, $E_c$ $=$100 v
Modulation index, ma $=$0.4
Power, P $=$?
We know that Power, $P_c$ $=$ $\dfrac{{{E_c}^2}}{{2R}}$
Substituting the values, we get
$\Rightarrow$ $P_c$ $=$ $\dfrac{{\left( {{{100}^2}} \right)}}{{2 \times 100}}$ $=$50 watt
Power is given by the formula, P $= $$\left( {1 + \dfrac{{{m_a}^2}}{2}} \right) P_c Substituting the values, we get \Rightarrow P =$$\left( {1 + \dfrac{{{{(0.4)}^2}}}{2}} \right)$ $50$
$\Rightarrow$ $P$ = $54 watt$
$\therefore$ $Power$ = $54 watt$

Hence the correct option is B.

Note: 1. The power of the amplitude modulation wave is equal to the sum of powers of the carrier, upper sideband, and lower sideband frequency components.
2. Amplitude Modulation was developed during the 20th century beginning with Roberto Landell De Moura and Reginald Fessenden’s radiotelephone experiments. It was the earliest method used for transmitting audio in radio broadcasting. In amplitude modulation, the strength or amplitude of the carrier oscillations is varied.
3. Amplitude Modulation is sometimes also called double-sideband amplitude modulation.
4. The modulation index describes how much the modulated variable of the carrier signal varies around the unmodulated level. In simple terms, we can also define it as the measure of amplitude variation about an unmodulated carrier.
5. In telecommunications and electronics, amplitude modulation means varying some aspect of the continuous wave carrier signal with an information-bearing modulation waveform. The message signal is extracted from the modulated carrier by demodulation at the receiving station.