91Ó°ÊÓ

In a transformer circuit, the turns ratio is a fundamental concept that expresses the relationship between the number of turns in the primary coil (\( N_p \)) and the secondary coil (\( N_s \)). This ratio is essential because it determines how voltage and current are transformed between circuits. To calculate it, you use the formula:

• Turns Ratio, \( n = \frac{N_p}{N_s} \)

For example, if a transformer has 1200 turns on the primary and 28 turns on the secondary, the turns ratio is:\[ n = \frac{1200}{28} \approx 42.86 \]This means that for every turn in the secondary coil, there are about 42.86 turns in the primary coil. This ratio helps in determining how a transformer's voltage and current characteristics will change. By understanding the turns ratio, you can predict how voltage decreases from the primary to the secondary or vice-versa.

To find the secondary voltage (\( V_s \)), you need to know the primary voltage (\( V_p \)) and the turns ratio (\( n \)). The relationship is given by:

• Secondary Voltage, \( V_s = \frac{V_p}{n} \)

In our exercise, we are given a primary voltage of 4800 V rms and a turns ratio of approximately 42.86. Substituting these values into the formula gives:\[ V_s = \frac{4800}{42.86} \approx 112 \text{ V rms} \]This formula shows how the primary voltage gets reduced over the secondary winding of a transformer. The smaller number of turns in the secondary results in a lower output voltage. This voltage is referred to as the secondary voltage and is what is available across the secondary winding for the load.

To solve for the currents in both the primary and secondary transformers, Ohm's Law plays a crucial role. Firstly, to find the secondary current (\( I_s \)), use the formula:

• \( I_s = \frac{V_s}{R} \), where \( V_s \) is the secondary voltage and \( R \) is the load resistance.

For our problem:\[ I_s = \frac{112}{10} = 11.2 \text{ A} \]
For the primary current (\( I_p \)), the turns ratio helps us relate it to the secondary current:

• \( I_p = \frac{I_s}{n} \)

Substituting the known values:\[ I_p = \frac{11.2}{42.86} \approx 0.261 \text{ A} \]This highlights how the current is inversely proportional to the turns ratio in a transformer. A higher secondary current results in a lower primary current due to the higher number of turns in the primary coil.

To determine the power supplied to the load, we apply the formula for power, which is the product of voltage and current:

• Power, \( P = V_s \times I_s \)

In this scenario, with a secondary voltage of 112 V and a secondary current of 11.2 A, the power supplied to the load is calculated as follows:\[ P = 112 \times 11.2 = 1254.4 \text{ W} \]This indicates that the total effective power received by the load is 1254.4 watts. Understanding this calculation is important as it reflects the capability of the transformer to transfer electrical power from the primary circuit, through the transformer, to the secondary load. It assures that the load connected can efficiently operate with the power supplied.