What turns ratio is required for a transformer to match a source impedance of 500 ohms to a load of 10 ohms?

What turns ratio is required for a transformer to match a source impedance of 500 ohms to a load of 10 ohms?

• A. 7.1 to 1
• B. 7 to 1
• C. 14 to 1
• D. None of the above

Answer: (A)

To find the required turns ratio for a transformer to match a source impedance of 500 ohms to a load of 10 ohms, you can use the formula for impedance transformation, which is based on the square of the turns ratio. The relationship is given by: \[ \text{Turns Ratio}^2 = \frac{Z_{source}}{Z_{load}} \] In this case, the source impedance is 500 ohms and the load impedance is 10 ohms. Plugging these values into the formula gives: \[ \text{Turns Ratio}^2 = \frac{500}{10} = 50 \] To find the turns ratio, you take the square root of both sides: \[ \text{Turns Ratio} = \sqrt{50} \approx 7.07 \] This value can be reasonably approximated as 7.1 when rounded to one decimal place. Therefore, the required turns ratio to match a source impedance of 500 ohms to a load of 10 ohms is approximately 7.1 to 1, confirming that the selected answer is correct. While other options may be close or represent common values, they do not accurately reflect the calculation needed for this specific

To find the required turns ratio for a transformer to match a source impedance of 500 ohms to a load of 10 ohms, you can use the formula for impedance transformation, which is based on the square of the turns ratio. The relationship is given by:

[ \text{Turns Ratio}^2 = \frac{Z_{source}}{Z_{load}} ]

In this case, the source impedance is 500 ohms and the load impedance is 10 ohms. Plugging these values into the formula gives:

[ \text{Turns Ratio}^2 = \frac{500}{10} = 50 ]

To find the turns ratio, you take the square root of both sides:

[ \text{Turns Ratio} = \sqrt{50} \approx 7.07 ]

This value can be reasonably approximated as 7.1 when rounded to one decimal place. Therefore, the required turns ratio to match a source impedance of 500 ohms to a load of 10 ohms is approximately 7.1 to 1, confirming that the selected answer is correct.

While other options may be close or represent common values, they do not accurately reflect the calculation needed for this specific