Question 3-18B4

To match impedances with a transformer, the turns ratio (N) is related to the square root of the impedance ratio. Specifically, the turns ratio from the primary (source) to the secondary (load) is given by the formula: $N = \sqrt{Z_{primary} / Z_{secondary}}$ In this case, the source impedance ($Z_{primary}$) is 500 ohms, and the load impedance ($Z_{secondary}$) is 10 ohms. $N = \sqrt{500 \text{ ohms} / 10 \text{ ohms}}$ $N = \sqrt{50}$ Calculating the square root of 50 gives approximately 7.071. Rounded to one decimal place, this is 7.1. Therefore, a turns ratio of 7.1 to 1 is required. Options B and C are incorrect because their square would yield impedance ratios significantly different from 50 (e.g., $14.2^2 \approx 201$, $50^2 = 2500$).