Question

A power amplifier has an output of 100 W and an input of 10 W. What is the power gain in decibels?
Group of answer choices

1

5

10

2

Answer 1

To calculate the power gain in decibels (dB), you can use the following formula:

\[
\text{Power Gain (dB)} = 10 \times \log_{10} \left( \frac{\text{Pout}}{\text{Pin}} \right)
\]

Where:
- \( \text{Pout} \) is the output power
- \( \text{Pin} \) is the input power

In this case:
- \( \text{Pout} = 100 \, \text{W} \)
- \( \text{Pin} = 10 \, \text{W} \)

Now plug in the values:

\[
\text{Power Gain (dB)} = 10 \times \log_{10} \left( \frac{100}{10} \right)
\]

This simplifies to:

\[
\text{Power Gain (dB)} = 10 \times \log_{10} (10)
\]

Since \( \log_{10} (10) = 1 \):

\[
\text{Power Gain (dB)} = 10 \times 1 = 10 \, \text{dB}
\]

So the power gain in decibels is **10 dB**.

The correct answer is **10**.