A cable has a loss of 6 dB. What percentage of its input power will appear at the output?

Group of answer choices

75%

90%

25%

50%

1 answer

To determine how much power remains at the output of a cable with a loss of 6 dB, we can use the formula that relates decibels to power:

\[ \text{Loss (dB)} = 10 \times \log_{10} \left( \frac{P_{\text{input}}}{P_{\text{output}}} \right) \]

Given that the loss is 6 dB, we can rearrange the formula to find the ratio of input power to output power:

\[ 6 = 10 \times \log_{10} \left( \frac{P_{\text{input}}}{P_{\text{output}}} \right) \]

Dividing both sides by 10:

\[ 0.6 = \log_{10} \left( \frac{P_{\text{input}}}{P_{\text{output}}} \right) \]

Now, we exponentiate both sides:

\[ 10^{0.6} = \frac{P_{\text{input}}}{P_{\text{output}}} \]

Calculating \(10^{0.6}\):

\[ 10^{0.6} \approx 3.981 \]

This indicates that:

\[ \frac{P_{\text{input}}}{P_{\text{output}}} \approx 3.981 \]

To find the output power as a percentage of the input power, we can express it as:

\[ \frac{P_{\text{output}}}{P_{\text{input}}} = \frac{1}{3.981} \approx 0.251 \]

Converting this to a percentage:

\[ \frac{P_{\text{output}}}{P_{\text{input}}} \times 100 \approx 25.1% \]

Thus, the percentage of input power that appears at the output is approximately 25%.

So the correct choice from the given options is:

25%