An input-to-output power ratio of 10:1 corresponds to what input-to-output voltage ratio?

To understand why an input-to-output power ratio of 10:1 corresponds to an input-to-output voltage ratio of 3.162:1, it's essential to delve into the relationship between power and voltage in electrical systems.

Power (P) is related to voltage (V) and resistance (R) through the formula P = V² / R. When comparing power ratios to voltage ratios, we can infer a relationship between them. If the power ratio is defined as P_out / P_in = 10 (or 10:1), we need to express this in terms of voltage.

Using the formula for power:

P_out / P_in = (V_out² / R) / (V_in² / R) = V_out² / V_in²

Here, the resistance cancels out, simplifying our relationship to:

V_out² / V_in² = 10

To find the voltage ratio:

(V_out / V_in)² = 10 V_out / V_in = √10

Calculating the square root of 10 gives approximately 3.162. Therefore, when we express the voltage ratio in relation to the initial power ratio of 10:1, we find that it simplifies to an input