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.