Question

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ________. (round off to nearest integer)

Hint:

To calculate the power loss in decibels, use the formula: \[ \text{Power Loss (dB)} = 10 \times \log_{10} \left( \frac{P_{\text{input}} - P_{\text{output}}}{P_{\text{output}}} \right). \]

Answer 1

Correct Answer: 13

The power loss in decibels can be calculated using the formula: \[ \text{Power Loss (dB)} = 10 \times \log_{10} \left( \frac{P_{\text{input}} - P_{\text{output}}}{P_{\text{output}}} \right) \] Given that 5% of the supplied power reaches the output, this means that \( P_{\text{output}} = 0.05 \times P_{\text{input}} \). Therefore, the power loss is: \[ P_{\text{loss}} = P_{\text{input}} - P_{\text{output}} = P_{\text{input}} - 0.05 \times P_{\text{input}} = 0.95 \times P_{\text{input}} \] Substitute the values into the formula: \[ \text{Power Loss (dB)} = 10 \times \log_{10} \left( \frac{0.95 \times P_{\text{input}}}{0.05 \times P_{\text{input}}} \right) = 10 \times \log_{10} (19) \approx 13.03 \, \text{dB}. \] Thus, the power loss in decibels is \( \boxed{13} \) dB.