Electrical Energy & Power

George Meshveliani

Lesson Plan

What is Electrical Power?
What is Electrical Energy?
The Problem of Energy Transfer.
The Power Triangle.
Units of Measurement: Watt & kWh.
Calculating the Cost of Electricity.
Common Appliance Costs.
Energy Consumption Graphs.
Practice Problems.
Interactive Quiz.

What is Electrical Power?

Power ($P$) is the rate at which electrical energy is transferred or used. It's how "fast" a device works. Think of a light bulb's brightness.

$$P = VI$$

Unit: Watt (W).

What is Electrical Energy?

Energy ($E$) is the total amount of power consumed over a period of time. It's what you pay for on your electricity bill.

0.00 kWh

$$E = Pt$$

Unit: Joule (J) or Kilowatt-hour (kWh).

The Problem of Energy Transfer

When electrical energy is transferred, some of it is lost as heat due to the resistance ($R$) of the wires. This is called **Joule heating**.

$$P_{loss} = I^2R$$

The higher the current or resistance, the more power is lost.

The Power Triangle

Just like Ohm's Law, there are multiple ways to calculate power.

P

V

I

$P = VI$
$P = I^2R$
$P = \frac{V^2}{R}$

Units of Measurement

Power is measured in Watts (W). A kilowatt (kW) is 1,000 W.

Energy is measured in Joules (J) or, more commonly for billing, Kilowatt-hours (kWh).

Conversion: $1 \, \text{kWh} = 3.6 \times 10^6 \, \text{J}$

A 1,000 W appliance running for 1 hour uses 1 kWh of energy.

Calculating the Cost of Electricity

To find the cost, you need three things:

Power of the appliance (in kW).
Time it is used (in hours).
Rate from your electricity provider ($/kWh).

$$Cost = \text{Energy (kWh)} \times \text{Rate ($/kWh$)}$$

Common Appliance Costs

This table shows the approximate daily cost of running common household appliances, based on a rate of $0.15/kWh$.

Appliance	Power (W)	Time Used/Day (h)	Daily Energy (kWh)	Daily Cost ($)
Television	200	4	0.8	0.12
Refrigerator	150	24	3.6	0.54
Microwave	1200	0.25	0.3	0.05
Laptop Charger	50	8	0.4	0.06

Appliance Power Comparison

A bar chart showing the power consumption of different appliances.

Energy Consumption Over Time

A line graph showing how total energy (kWh) accumulates as a device runs.

Practice Problem 1 (Power)

A television draws $2 \, \text{A}$ of current from a standard $120 \, \text{V}$ outlet. What is the power consumed by the television?

Hint: Use the formula $P = VI$.

Solution to Problem 1

Using the power formula:

$$P = V \times I$$

$$P = 120 \, \text{V} \times 2 \, \text{A} = 240 \, \text{W}$$

The television consumes $240 \, \text{W}$ of power.

Practice Problem 2 (Energy & Cost)

An air conditioner has a power rating of $1500 \, \text{W}$. If it runs for 8 hours a day, and the electricity rate is $0.15$ per kWh, what is the cost to run it for one day?

Hint: Convert Watts to kilowatts, then calculate energy and cost.

Solution to Problem 2

Step 1: Convert power to kW.

$$P(\text{kW}) = \frac{1500 \, \text{W}}{1000} = 1.5 \, \text{kW}$$

Step 2: Calculate the total energy consumed.

$$E = P \times t = 1.5 \, \text{kW} \times 8 \, \text{h} = 12 \, \text{kWh}$$

Step 3: Calculate the cost.

$$Cost = 12 \, \text{kWh} \times 0.15 \, \text{$ /kWh} = 1.80 \, \text{$}$$

Practice Problem 3 (Power Loss)

A power line has a resistance of $0.5 \, \Omega$ and carries a current of $20 \, \text{A}$. How much power is lost as heat in the wire?

Hint: Use the formula for power loss, $P_{loss} = I^2R$.

Solution to Problem 3

Using the power loss formula:

$$P_{loss} = I^2 \times R$$

$$P_{loss} = (20 \, \text{A})^2 \times 0.5 \, \Omega$$

$$P_{loss} = 400 \times 0.5 = 200 \, \text{W}$$

The power lost as heat is $200 \, \text{W}$.

Interactive Quiz

Summary

Power ($P$) is the rate of energy transfer, measured in Watts (W).
Energy ($E$) is the total power used over time, measured in Joules (J) or Kilowatt-hours (kWh).
Heat Loss: Some energy is lost as heat due to resistance, calculated by $P_{loss} = I^2R$.
Formulas: $P = VI$ and $E = Pt$.
Cost: Calculated by multiplying energy (kWh) by the rate ($/kWh$).

Thank You

Any questions?