Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Define power, energy, and efficiency with their SI units.
• Calculate electrical power using P = VI, P = I²R, and P = V²/R.
• Calculate electrical energy consumption and cost.
• Calculate the efficiency of electrical devices.
• Apply these concepts to simple electrical circuits.

Lesson summary

This week, we delve deeper into the fundamental electrical principles of power, energy, and efficiency. These concepts are not just theoretical; they underpin everything from the functioning of your cell phone charger to the national electricity grid (Eskom) that powers our homes and industries. Understanding power, energy, and efficiency allows us to analyze electrical circuits, optimize energy consumption, and make informed decisions about electrical appliances and systems. Given South Africa's ongoing challenges with electricity supply and load shedding, understanding energy efficiency is crucial for both individuals and the country as a whole.

Lesson notes

Power (P)

Definition: Power is the rate at which electrical energy is transferred or consumed in a circuit. It essentially tells us how quickly electrical energy is being used.

Unit: The SI unit of power is the watt (W). One watt is equal to one joule per second (1 W = 1 J/s).

Formulas: There are three primary formulas for calculating power, depending on the information available: P = VI: Power (watts) = Voltage (volts) x Current (amperes) P = I²R: Power (watts) = Current (amperes)² x Resistance (ohms) P = V²/R: Power (watts) = Voltage (volts)² / Resistance (ohms)

Explanation: The first formula (P = VI) is fundamental. It shows that power is directly proportional to both voltage and current. Increasing either voltage or current will increase the power. The other two formulas are derived from Ohm's Law (V = IR) and are useful when either voltage or current is unknown, but resistance is known.

Energy (E)

Definition: Energy is the capacity to do work. In the context of electricity, it's the total amount of electrical work done.

Unit: The SI unit of energy is the joule (J).

However, in electrical contexts, especially when dealing with larger amounts of energy, the kilowatt-hour (kWh) is more commonly used.

Relationship with Power: Energy is related to power by the following formula: E = Pt: Energy (joules or kWh) = Power (watts or kW) x Time (seconds or hours)

Kilowatt-hour (kWh): 1 kWh is the amount of energy consumed by a 1 kW device operating for 1 hour. It's the unit used by Eskom for billing electricity consumption.

Explanation: Energy consumption is directly proportional to both power and time. A more powerful device will consume more energy in the same amount of time, and a device operating for a longer time will consume more energy. Efficiency (η)

Definition: Efficiency is the ratio of useful output power to the total input power of a device or system. It indicates how well a device converts input energy into useful output energy, with minimal waste.

Unit: Efficiency is usually expressed as a percentage (%).

Formula: η = (Output Power / Input Power) x 100% Explanation: No device is perfectly efficient. Some energy is always lost, usually as heat, sound, or friction. A higher efficiency means less energy is wasted. Efficiency is crucial for saving energy and reducing costs. For example, an energy-efficient light bulb will produce the same amount of light as an inefficient bulb, but consume less electricity.

Worked example

Example 1: Calculating Power

A cellphone charger supplies 5V to a cellphone, and the cellphone draws a current of 2A. Calculate the power consumed by the cellphone.

Solution:

P = VI

P = 5V x 2A

P = 10W

Therefore, the cellphone consumes 10 watts of power.

Example 2: Calculating Energy Consumption and Cost