An industrial load consumes 100 kW at 0.8 PF lagging. The line voltage is 480 V rms. If the li

step 1 In this problem, the value of PL is equal to VRMS multiplication IRMS multiplication PF, which i

An industrial load consumes 100 kW at 0.8 PF lagging. The...

An industrial load consumes $100 \mathrm{~kW}$ at $0.8 \mathrm{PF}$ lagging. The line voltage is $480 \mathrm{~V} \mathrm{rms}$. If the line resistance between the generator and load is $0.1 \Omega$, find the transmission line losses.

Key Concepts

Power Factor

Power factor is the ratio of real power (the useful power actually consumed by the load) to apparent power (the product of RMS voltage and current) in an AC circuit. It indicates how effectively electrical power is being used and has a direct impact on the current drawn by the load, which in turn affects power losses in the transmission system.

Apparent Power

Apparent power represents the total power supplied to an AC circuit, calculated as the product of the RMS voltage and the current. It is a combination of real power and reactive power, and is typically higher than the real power when the power factor is less than one, influencing how much current flows through the system.

Transmission Line Losses

Transmission line losses refer to the power dissipated as heat in the resistance of the transmission line. These losses are generally determined using the I²R formula, where lowering the current (by improving power factor or adjusting load characteristics) can significantly reduce the energy lost in transmission.

RMS Voltage and Ohm’s Law in AC Circuits

RMS (root mean square) voltage is a measure of the effective voltage in an AC circuit. Using Ohm’s Law for AC circuits, the current can be calculated by dividing the voltage by the impedance, and when the impedance is predominantly resistive, this simplifies the analysis of line losses using the line resistance and the computed current.

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