Which decibel value most closely represents a power increase from 5 watts to 10 watts?

Which decibel value most closely represents a power increase from 5 watts to 10 watts?

• A. 2 dB
• B. 3 dB
• C. 5 dB
• D. 10 dB

Answer: (B)

The increase in power from 5 watts to 10 watts represents a doubling of power. In decibel terms, an increase of 3 dB corresponds to doubling the power of a signal. To understand this in a practical sense, the decibel (dB) scale is logarithmic, meaning it measures ratios. The formula to calculate the decibel change for power is given by: \[ \text{dB} = 10 \times \log_{10} \left( \frac{P_2}{P_1} \right) \] where \(P_2\) is the final power (10 watts) and \(P_1\) is the initial power (5 watts). Plugging the values into the formula gives: \[ \text{dB} = 10 \times \log_{10} \left( \frac{10}{5} \right) = 10 \times \log_{10} (2) \approx 10 \times 0.301 = 3.01 \text{ dB} \] This rounds to approximately 3 dB, confirming the assertion that a doubling of power results in an increase of about 3 dB.

The increase in power from 5 watts to 10 watts represents a doubling of power. In decibel terms, an increase of 3 dB corresponds to doubling the power of a signal.

To understand this in a practical sense, the decibel (dB) scale is logarithmic, meaning it measures ratios. The formula to calculate the decibel change for power is given by:

[

\text{dB} = 10 \times \log_{10} \left( \frac{P_2}{P_1} \right)

]

where (P_2) is the final power (10 watts) and (P_1) is the initial power (5 watts). Plugging the values into the formula gives:

[

\text{dB} = 10 \times \log_{10} \left( \frac{10}{5} \right) = 10 \times \log_{10} (2) \approx 10 \times 0.301 = 3.01 \text{ dB}

]

This rounds to approximately 3 dB, confirming the assertion that a doubling of power results in an increase of about 3 dB.