If the input-to-output power ratio is 10:1, what is the corresponding input-to-output voltage ratio?

To find the corresponding input-to-output voltage ratio from a given input-to-output power ratio, you can use the relationship between power and voltage in electrical systems. Power (P) is proportional to the square of the voltage (V) across components, which can be represented mathematically as:

[ P \propto V^2 ]

This means that if you know the power ratio, you can determine the voltage ratio by taking the square root of the power ratio. In this case, the input-to-output power ratio is 10:1. To find the voltage ratio, you take the square root of this ratio:

[ \text{Voltage ratio} = \sqrt{10:1} ]

Calculating this gives:

[ \text{Voltage ratio} = \sqrt{10} = 3.162 ]

Thus, the input-to-output voltage ratio is 3.162:1. This corresponds with the correct answer. Understanding this relationship is important because it demonstrates how power and voltage are interlinked in electrical circuits, allowing us to derive one from the other using algebraic relationships.