91Ó°ÊÓ

Transformers are essential devices in electrical power systems for modifying voltage levels effectively. A key performance indicator for transformers is their efficiency. Efficiency in transformers is the ratio of output power to input power, expressed usually as a percentage. For a transformer with high efficiency, almost all the input power is transferred to the output, with minimal loss.
Transformer efficiency is affected by several factors, such as core losses and copper losses. Core losses occur in the transformer's iron core due to hysteresis and eddy currents. Copper losses arise from the resistance in the windings of the transformer. In general, maintaining high transformer efficiency is crucial for reducing energy loss in power systems.

Electrical resistance is a measure of the opposition that a material offers to the flow of electric current, usually measured in ohms (Ω). Resistance depends on the material's properties, its temperature, and its dimensions. For instance in wires used for power transmission, the resistance might increase with the length of the wire or decrease with a larger cross-sectional area.

• Resistance per unit length is crucial in calculating total resistance over long distances, like the wire resistance per kilometer given in the exercise.
• This principle allows for the estimation of power loss through the transmission wires, highlighting the importance of minimizing resistance in economic and efficient power networks.

Calculating power loss is essential for understanding the efficiency of power transmission. Power loss in a transmission line can be determined using the formula \( P_{\text{loss}} = I^2R \), where \( I \) is the current through the wires, and \( R \) is the resistance of the wires.
High currents lead to significant power losses, as shown by the exercise where power loss is 700,000 W without a transformer, and only 70 W after using a step-up transformer. This reduction occurs because raising the voltage substantially decreases the current for the same power, thereby reducing losses.

A step-up transformer increases voltage from the primary side (input) to the secondary side (output). It is commonly used in power distribution to boost voltage levels and thus reduce current levels, minimizing energy losses across long transmission lines.
In the exercise, the 100:1 step-up transformer increases the transmission voltage from 1200 V to 120,000 V. This increase drastically reduces the current needed to transmit the same amount of power, thereby minimizing power losses significantly in the transmission wires.

Ohm's Law is a fundamental principle in electricity that shows a relationship between voltage, current, and resistance. It is expressed as \( V = IR \), where \( V \) is the voltage across the device, \( I \) is the current through the device, and \( R \) is the resistance.

• Ohm's Law helps calculate how much current will flow through a circuit given the voltage and resistance, which is crucial during power transmission design decisions.
• Understanding this law is vital for calculating power distribution as shown in this exercise, where using a higher voltage (and thereby lower current) leads to decreased power loss.