Suppose there are two transformers between your house and...

Suppose there are two transformers between your house and the high-voltage transmission line that distributes the power. In addition, assume your house is the only one using electric power. At a substation the primary of a step-down transformer (turns ratio $=1: 29$ ) receives the voltage from the high-voltage transmission line. Because of your usage, a current of $48 \mathrm{~mA}$ exists in the primary of this transformer. The secondary is connected to the primary of another step-down transformer (turns ratio $=1: 32)$ somewhere near your house, perhaps up on a telephone pole. The secondary of this transformer delivers a $240-\mathrm{V}$ emf to your house. How much power is your house using? Remember that the current and voltage given in this problem are rms values.

Key Concepts

Power Calculation

Electrical power is the product of voltage and current (P = V x I) and is fundamental in assessing energy consumption in AC circuits. Using rms values for voltage and current ensures that the calculated power accurately reflects the energy delivered or consumed over time.

Conservation of Power in Transformers

In an ideal transformer, the power on the primary side (input) is equal to the power on the secondary side (output), meaning that the product of voltage and current remains constant across the transformer. This principle allows for the determination of unknown electrical quantities when other parameters are known.

Turns Ratio

The turns ratio of a transformer, which is the ratio of turns in the primary coil to turns in the secondary coil, determines the relationship between the input and output voltages and currents. A higher turns ratio in a step-down transformer results in a lower output voltage and a proportionally higher output current, assuming ideal conditions.

RMS Values in AC Circuits

Root Mean Square (rms) values are used in AC circuits to represent the effective or equivalent DC values of voltage and current, which are crucial for calculating power consumption. They account for the time-varying nature of AC signals and are used to ensure accurate power calculations in electrical systems.

Transformers

A transformer is an electrical device that transfers energy between circuits through electromagnetic induction. It is used to change voltage levels, allowing electrical power to be transmitted efficiently over long distances and then stepped down to safer, usable levels for consumers.

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