Question

The output voltage of a 54-W transformer is 10 V, and the input current is 25 A. Assume 100% efficiency. What is the transformer's turns ratio?

a) 0.2
b) 2.5
c) 5.4
d) 54

Answer 1

To calculate the transformer's turns ratio, first calculate the input voltage using the power and input current. Then, divide the output voltage by the input voltage to get the turns ratio. The closest answer given the options is 5.4.

Step-by-step explanation:

The question asks for the transformer's turns ratio given that the output voltage is 10 V, the input current is 25 A, and the transformer has a power of 54 W. Since the transformer's efficiency is assumed to be 100%, the power in equals the power out. Therefore, we can first calculate the input voltage (Vin) using the transformer's power (P) and the input current (Iin) given by P = Vin × Iin. After finding the input voltage, we use the relationship of transformer turns ratio (N = Vout/Vin) to find the turns ratio.

Using the power formula, the input voltage Vin can be calculated as follows:

P = Vin × Iin
54 W = Vin × 25 A
Vin = 54 W / 25 A
Vin = 2.16 V

Now, the transformer's turns ratio (N) is:

N = Vout/Vin
N = 10 V / 2.16 V
N = 4.63

This ratio does not exactly match any of the multiple-choice options provided, suggesting there might be a typo or an error in the options or question details. However, rounding to the nearest option, the closest answer is option c) 5.4.