Question

A transformer on a pole near a factory steps the voltage down from 3,600 V(rms) to 120 V (rms). The transformer is to deliver 1950 kW to the factory at 80% efficiency. Find the power delivered to the primary.

Answer 1

Given an efficiency of 80% and a secondary power output of 1950 kW, the power delivered to the primary of the transformer is calculated to be 2437.5 kW.

Step-by-step explanation:

The student's question is about calculating the power delivered to the primary coil of a transformer that is used by a factory, given its secondary output power and efficiency. To find the power delivered to the primary of the transformer, we use the formula involving efficiency: Efficiency = (Power Output / Power Input) * 100%. Rearranging this formula to solve for Power Input, we get: Power Input = Power Output / Efficiency. With the given efficiency of 80% (or 0.8 when converted to a decimal), and a power output of 1950 kW, the calculation is as follows: Power Input = 1950 kW / 0.8 = 2437.5 kW. Hence, the power delivered to the primary is 2437.5 kW. This calculation assumes ideal conditions where the efficiency accounts for all losses, including any potential power losses in the transmission line.