Which decibel value represents a power decrease from 12 watts to 3 watts?

Which decibel value represents a power decrease from 12 watts to 3 watts?

• A. 0 dB
• B. -3 dB
• C. -6 dB
• D. 3 dB

Answer: (C)

To determine the decibel value that represents a power decrease from 12 watts to 3 watts, it is crucial to understand how decibels (dB) quantify power ratios. The formula to calculate the decibel change based on power is: \[ \text{dB} = 10 \log_{10} \left( \frac{P_2}{P_1} \right) \] In this case, \( P_1 \) is the initial power (12 watts) and \( P_2 \) is the final power (3 watts). Plugging the values into the formula gives: \[ \text{dB} = 10 \log_{10} \left( \frac{3}{12} \right) = 10 \log_{10} (0.25) \] Calculating \( \log_{10} (0.25) \): - The value of \( \log_{10} (0.25) \) is equal to \( -0.602 \) (since \( 0.25 \) can be expressed as \( 1/4 \), and \( \log_{10} (1/4) = -\log

To determine the decibel value that represents a power decrease from 12 watts to 3 watts, it is crucial to understand how decibels (dB) quantify power ratios. The formula to calculate the decibel change based on power is:

[

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

]

In this case, ( P_1 ) is the initial power (12 watts) and ( P_2 ) is the final power (3 watts). Plugging the values into the formula gives:

[

\text{dB} = 10 \log_{10} \left( \frac{3}{12} \right) = 10 \log_{10} (0.25)

]

Calculating ( \log_{10} (0.25) ):

• The value of ( \log_{10} (0.25) ) is equal to ( -0.602 ) (since ( 0.25 ) can be expressed as ( 1/4 ), and ( \log_{10} (1/4) = -\log