An AC power generator produces 50. A (rms) at 3 600 V. The...

An AC power generator produces 50. A (rms) at 3 600 V. The voltage is stepped up to $1.0 \times 10^{5} \mathrm{V}$ by an ideal transformer, and the energy is transmitted through a long - distance power line that has a resistance of $100 . \Omega$ What percentage of the power delivered by the generator is dissipated as heat in the power line?

An AC power generator produces 50. A (rms) at 3 600 V. The voltage is stepped up to $1.0 \times 10^{5} \mathrm{V}$ by an ideal transformer, and the energy is transmitted through a long - distance power
line that has a resistance of $100 . \Omega$ What percentage of the power delivered by the generator is dissipated as heat in the power line?

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Key Concepts

AC Power Analysis

In AC systems, power is often calculated using the root-mean-square (rms) values of voltage and current. This concept ensures that the power delivered is evaluated based on effective values that account for the time-varying nature of AC signals, allowing for accurate power measurements in circuits and devices.

Ideal Transformer Operation

An ideal transformer changes voltage and current levels while conserving power, meaning that the input power equals the output power (neglecting losses). By stepping up voltage, the current is proportionally reduced, which is a key principle for minimizing losses during long-distance power transmission.

Joule Heating

Joule heating refers to the power loss in electrical conductors due to resistance, computed as the product of the square of the current and the resistance (I²R). This concept is essential in understanding energy dissipation in conductive lines and determining the efficiency of electrical transmission.

Electrical Power Transmission Efficiency

Effective power transmission involves minimizing energy losses during distribution. By using high voltage to reduce the current, the resistive losses in the transmission lines (proportional to I²R) are significantly decreased, thereby improving the overall efficiency and reducing waste heat energy.

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