A transformer on a pole near a factory steps the voltage...

A transformer on a pole near a factory steps the voltage down from 3600 V (rms) to 120 V (rms). The transformer is to deliver $1.0 \times 10^{3} \mathrm{kW}$ to the factory at 90% efficiency. Find (a) the power delivered to the primary, (b) the current in the primary, and (c) the current in the secondary.

A transformer on a pole near a factory steps the voltage down from 3600 V (rms) to 120 V (rms). The transformer is to deliver $1.0 \times 10^{3} \mathrm{kW}$ to the factory at 90% efficiency. Find
(a) the power delivered to the primary, (b) the current in the primary, and (c) the current in the secondary.

Key Concepts

Transformer Operation

A transformer is an electrical device that transfers energy between circuits through the principle of electromagnetic induction. It is used to change voltage levels in AC circuits, facilitating efficient power transmission and distribution across different parts of an electrical network.

Turns Ratio and Voltage Transformation

The turns ratio of a transformer, which is the ratio of the number of windings on the primary coil to the secondary coil, determines how the voltage is modified between the two sides. This ratio establishes the proportional relationship between the primary and secondary voltages, allowing the transformer to step up or step down AC voltages as needed.

Transformer Efficiency

Efficiency in a transformer is the measure of how well it transfers energy from the primary to the secondary circuit, defined as the ratio of output power to input power. Real transformers incur losses due to factors such as heat, meaning that efficiency is typically less than 100%, and these losses must be considered in power calculations.

AC Power Calculation using RMS Values

AC power calculations commonly use root mean square (RMS) values for voltage and current because these values represent the effective energy or power that would be delivered by an equivalent DC supply. The power in an AC circuit is determined by the product of the RMS voltage and the RMS current.

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