Final answer:
To calculate the power supplied to an industrial load through a transmission line, we can use the line voltage and impedance. By substituting the given values into the formula for power, we can determine the power supplied to the load.
Step-by-step explanation:
A transformer supplies power to an industrial load through a transmission line with a line impedance of 0.1 + j0.2 Ω. The line voltage at the load is 480∠0° Vrms. To determine the power supplied to the load, we can use the voltage and the line impedance. We can calculate the power using the formula P = Vrms^2 / Z, where P is the power, Vrms is the voltage rms value, and Z is the impedance.
Substituting the given values, we get P = (480^2) / (0.1 + j0.2), where j is the imaginary unit. To simplify, we need to find the complex conjugate of the impedance, which is 0.1 - j0.2. Multiplying the numerator and denominator by the complex conjugate, we get P = (480^2 * (0.1 - j0.2)) / ((0.1 + j0.2) * (0.1 - j0.2)).
Using the formula (a +- bi)(a -+ bi) = a^2 + b^2, we can simplify the denominator to 0.1^2 + 0.2^2 = 0.05. Substituting this value, we get P = (480^2 * (0.1 - j0.2)) / 0.05, which simplifies to P = 0.05 * (480^2 * (0.1 - j0.2)). Calculating this expression gives the power supplied to the load.