An amplifier rated at 30 w output is connected to a speaker whose impedance is 1

Question

An amplifier rated at 30 w output is connected to a speaker whose impedance is 10.

1. If the power gain of the amplifier is +42dB, what is the input power required to obtain the full output from the amplifier?
2.If the voltage gain of the amplifier is 60dB, what is the required input voltage if the amplifier is to produce its rated output?

Need details. Thank you!!!

Explanation / Answer

so 30 Watts is at the output of the ampflier... and its power gain is 42 dB. 42 dB is a power gain of 10^(42/10 ) = 15 848.9319 Input power * 15 848.9319 = Output power input power * 15848.9319 = 30 Watts so the input power = 1.89 mW (this is mili watts) part 2. if the the voltage gain is 60 dB, what is the required input voltage to produce the rated 30 watts. for a sinusoidal waveform of the form V * cos (2*pi*t) , the power delivered at the load is 1/2 * V^2 / R where R is the 10 Ohm from the speaker if 1/2 V^2/R = 30 watts , --> solve for V = 24.49 V 60 dB in voltage gain is a factor of 10^(60/20) = 1000 so the input voltage peak amplitude must be 24.49 / 1000 = 24.49 mV

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