Question 6A246

A transformer's turns ratio directly relates to its voltage and current transformation capabilities. The ratio of primary to secondary voltage is equal to the turns ratio (Vp/Vs = Np/Ns), while the ratio of primary to secondary current is inversely proportional to the turns ratio (Ip/Is = Ns/Np). Impedance (Z) is defined as voltage divided by current (Z = V/I). Therefore, the impedance ratio across a transformer (Zp/Zs) can be expressed as (Vp/Vs) divided by (Ip/Is). Substituting the turns ratio relationships, we get Zp/Zs = (Np/Ns) / (Ns/Np), which simplifies to (Np/Ns) * (Np/Ns) = (Np/Ns)$^2$. To find the turns ratio, we take the square root of both sides: Np/Ns = $\sqrt{\text{Zp/Zs}}$. Thus, the turns ratio varies as the square root of the impedance ratio. Options B, C, and D are incorrect because they do not reflect this fundamental squared relationship in impedance transformation.