Lesson Notes By Weeks and Term v5 - Grade 11
Electrical principles: power, energy and efficiency – Week 4 focus
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Electrical principles: power, energy and efficiency – Week 4 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Electrical Technology
Class: Grade 11
Term: 1st Term
Week: 4
Theme: General lesson support
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In this week's lesson, we'll delve into the fundamental electrical principles of power, energy, and efficiency. Understanding these concepts is absolutely crucial, not just for success in Electrical Technology, but also for being an informed and responsible citizen in South Africa. From understanding your household electricity bill to evaluating the performance of renewable energy systems, these principles are at play. Consider the load shedding challenges we face daily. Understanding power, energy, and efficiency helps us make informed decisions about energy conservation and alternative power sources, such as solar panels or generators, relevant to our South African context.
Power (P) Electrical power is the rate at which electrical energy is transferred by an electric circuit. It's essentially how quickly electrical work is being done. The unit of power is the Watt (W).
DC Circuits: In a DC (Direct Current) circuit, power is calculated using the following formulas: P = V I (Power = Voltage * Current) P = I² R (Power = Current squared * Resistance) P = V² / R (Power = Voltage squared / Resistance)
Where: P = Power (Watts) V = Voltage (Volts) I = Current (Amperes) R = Resistance (Ohms)
AC Circuits: In AC (Alternating Current) circuits, we need to consider the power factor (cos φ) because voltage and current are not always in phase.
Apparent Power (S): S = V I (Volt-Amperes - VA) This is the power seemingly delivered to the circuit.
Active Power (P): P = V I * cos φ (Watts - W) This is the actual power dissipated by the circuit, the power that does useful work.
Reactive Power (Q): Q = V I * sin φ (Volt-Amperes Reactive - VAR) This power is stored and returned to the source by reactive components (inductors and capacitors). It does not do useful work. cos φ is the power factor, representing the phase angle between voltage and current. Energy (E) Electrical energy is the capacity to do work, and it's measured in Joules (J).
However, in practical applications, especially when dealing with electricity bills, we often use the kilowatt-hour (kWh).
Relationship between Power and Energy: Energy is simply power used over a period of time. E = P t (Energy = Power * Time)
Where: E = Energy (Joules or kWh) P = Power (Watts or kW) t = Time (seconds or hours)
Conversion: 1 kWh = 3.6 x 10^6 Joules (3.6 MegaJoules) Efficiency (η) Efficiency is a measure of how effectively an electrical device or system converts input energy into useful output energy. It's expressed as a percentage.
Formula: η = (Output Power / Input Power) 100% Where: η = Efficiency (%) Output Power = Useful power delivered by the device or system Input Power = Total power supplied to the device or system Efficiency is always less than 100% due to losses (e.g., heat, friction, radiation) within the device or system. These losses are crucial to understand and minimize.
DC Circuit - Power Calculation:
A 12V DC motor draws a current of 2A. Calculate the power consumed by the motor.
Solution:
P = V I
P = 12V 2A
P = 24W
Therefore, the power consumed by the motor is 24 Watts.
Energy Consumption Calculation:
A 100W light bulb is used for 5 hours per day for 30 days. Calculate the total energy consumed in kWh and the cost if the electricity price is R2.50 per kWh.
Solution:
Total power consumed per day: 100W = 0.1 kW
Energy consumed per day: E = P t = 0.1 kW * 5 hours = 0.5 kWh
Total energy consumed in 30 days: 0.5 kWh/day 30 days = 15 kWh
Total cost: 15 kWh R2.50/kWh = R37.50