What is the relationship between voltage ratio and power ratio?

The relationship between voltage ratio and power ratio is well defined by the principle of power in electrical circuits. When analyzing electrical power in terms of voltage, the power (P) can be expressed as the product of voltage (V) and current (I) in the following way: P = V × I.

When considering the ratio of powers in two circuits, the power ratio can be expressed as the ratio of the voltages squared, assuming that the current remains constant. Mathematically, this can be represented by the following relationship:

If P1 and P2 are the powers of two circuits and V1 and V2 are their respective voltages, the power ratio can be expressed as:

P1 / P2 = (V1² / V2²)

This indicates that the power ratio is related to the square of the voltage ratio. Thus, if we take the voltage ratio V1 / V2 and square it, we find that:

(V1 / V2)² = P1 / P2

Taking the square root of both sides leads to the conclusion that the voltage ratio is equal to the square root of the power ratio, confirming the correctness of the answer given.

Therefore, the correct answer helps in understanding that