An amplifier has a 50 watt output and a 5 watt input. What is the gain in decibels for this amplifier, rounded to the nearest decibel?
Gain in dB = 10 log(50/5) = 10log10 = 10*1 = 10dB
To calculate the gain in decibels for an amplifier, we can use the formula:
Gain (in decibels) = 10 * log10(Pout / Pin),
where Pout is the output power and Pin is the input power.
In this case, Pout = 50 watts and Pin = 5 watts.
Plugging these values into the formula:
Gain (in decibels) = 10 * log10(50 / 5).
Calculating the ratio inside the logarithm:
Gain (in decibels) = 10 * log10(10).
Using a calculator to evaluate the logarithm:
Gain (in decibels) = 10 * 1.
Multiplying:
Gain (in decibels) = 10.
Therefore, the gain in decibels for this amplifier is 10, rounded to the nearest decibel.