Final answer:
To find the no-load voltage, calculate the power factor using the angle provided and the full-load voltage. Then, use the power factor to calculate the apparent power and the no-load current. Finally, use the no-load impedance and no-load current to find the no-load voltage.
Step-by-step explanation:
To find the no-load voltage, we need to consider the voltage drop due to the equivalent impedance of the transformer. The full load voltage of the transformer is given as 110 V and the full-load current lags the voltage by an angle of 32.5 degrees. From this information, we can calculate the power factor using the cosine of the angle:
power factor = cos(32.5) = 0.854
Since the transformer is operating at full load, the power factor will be the same for the no-load voltage. Therefore, we can calculate the apparent power by dividing the full-load power (P) by the power factor:
apparent power = P / power factor = 2000 VA / 0.854 = 2339.84 VA
Finally, we can use the apparent power and the full-load voltage to calculate the no-load current:
no-load current = apparent power / full-load voltage = 2339.84 VA / 110 V = 21.27 A
Given that the no-load current is purely reactive, we can calculate the no-load impedance using the formula:
no-load impedance = no-load voltage / no-load current = 0.364 ohm
Now we can rearrange the formula to solve for the no-load voltage:
no-load voltage = no-load impedance * no-load current = 0.364 ohm * 21.27 A = 7.752 V
Therefore, the no-load voltage of the transformer will be approximately 7.752 volts.