Answer:
To determine the output voltage of the transformer at the generating plant for a desired overall transmission efficiency, we need to consider the input voltage, output voltage, and the efficiency of the transformer.
Assuming a perfect transformer, the input power (Pin) is equal to the output power (Pout). The efficiency (η) of the transformer can be expressed as the ratio of the output power to the input power:
η = Pout / Pin
Since Pin = Pout for a perfect transformer, the efficiency can be written as:
η = 1
To achieve an overall transmission efficiency of 97.9% (0.979), we can set up the following equation:
η_total = η_transmission * η_transformer
0.979 = η_transmission * 1
Solving for η_transmission:
η_transmission = 0.979
Now, assuming the transmission efficiency (η_transmission) is known, we can calculate the required output voltage (Vout) at the generating plant.
η_transmission = Vout / Vin
0.979 = Vout / Vin
Solving for Vout:
Vout = 0.979 * Vin
Therefore, the output voltage at the generating plant should be 0.979 times the input voltage (Vin) to achieve an overall transmission efficiency of 97.9%, assuming a perfect transformer.
Step-by-step explanation: