If an electronic circuit experiences a loss of 3 decibels with an input power of 6 watts, what would its output power be, to the nearest watt?
To calculate the output power, we need to understand the concept of decibels (dB) and their relationship with power.
Decibels represent the logarithmic ratio of two power levels. When we say that the circuit experiences a loss of 3 decibels (dB), it means that the output power is 3 dB lower than the input power.
The formula to convert between decibels and power is:
dB = 10 * log10(P1 / P2)
Where:
- dB is the decibel value
- P1 is the initial power level (input power)
- P2 is the final power level (output power)
In this case, we know the input power, which is 6 watts, and the loss of 3 decibels. We need to calculate the output power.
To find the output power, we can rearrange the formula:
dB = 10 * log10(P1 / P2)
Divide both sides of the equation by 10:
dB / 10 = log10(P1 / P2)
Next, we can rewrite the equation in exponential form:
10 ^ (dB / 10) = P1 / P2
Now, substitute the known values:
10 ^ (3 / 10) = 6 / P2
Simplifying:
1.995 = 6 / P2
Cross-multiply:
P2 = 6 / 1.995
Calculating:
P2 ≈ 3.007
Rounding to the nearest watt, the output power would be approximately 3 watts.