Electric Power

Lesson 4 of 4: Electrical Circuits

In this lesson:

• Define electric power and calculate using
• Derive and
• Calculate energy costs and explain high-voltage transmission

Learning Objectives for This Lesson

By the end of this lesson, you should be able to:

1. Define electric power using
2. Derive and apply and
3. Calculate electrical energy consumption using
4. Explain why power lines use high voltage

Opening Question: A 60 W Light Bulb

A 60 W light bulb operates at 120 V.

• What current flows through it?
• What is its resistance?

Think — use the formulas you'll learn today.

Deriving the Electric Power Formula

• = power (W), = current (A), = potential difference (V)

Joule Heating — Why Resistors Get Warm

For a resistor: = electrical energy converted to heat per second

• Phone charger warm? → Current through resistors inside
• Electric heater? → Large current through high-resistance element
• Light bulb? → Resistance converts electrical energy to light and heat

Answer: The 60 W Light Bulb

Given: ,

Find current:

Find resistance:

Quick Check: Calculate the Device Power

A device draws 3 A from a 110 V outlet.

What is its power rating?

Three Forms of the Power Formula

Worked Example:

Given: A resistor carries and has

The resistor dissipates 80 watts as heat.

Worked Example:

Given: across a appliance

The appliance consumes 240 watts.

Quick Check: Choose the Right Formula

Two situations — which formula to use?

1. Resistance wire: , . Find .
2. Heating element: , . Find .

Energy Consumption:

• SI unit: joule (J) = watt-second (W·s)
• Practical unit: kilowatt-hour (kWh) = 1000 W × 3600 s = J
• Electricity bills are measured in kWh

Household Energy Audit by Appliance

Highest daily cost: air conditioner (1500 W × 6 h = 9 kWh/day)

Worked Example: Hair Dryer Cost

Hair dryer: , used for 20 min h, rate = $0.15/kWh

Energy:

Cost: (about 7.5 cents)

Quick Check: Calculate the TV Cost

A 100 W TV runs 4 hours per day. Rate = $0.15/kWh.

What is the daily energy cost?

Convert to kW, multiply by hours, multiply by rate.

Transmission Lines: The Power Loss Problem

Power plant delivers 1 MW over transmission lines with

Power lost in lines:

Goal: Minimize while delivering the same power to customers.

Worked Example: Transmit at 1,000 V

,

You lose more power in the lines than you deliver!

Worked Example: Transmit at 100,000 V

Increase V by 100 → decrease I by 100 → decrease by 10,000.

Quick Check: Effect of Doubling Voltage

For a fixed delivered power :

If voltage doubles (), what happens to:

• Current ?
• Line loss ?

Transformers Enable High-Voltage Power Transmission

Transformers (sec-20-3) change voltage levels for AC electricity:

• Step up at the power plant: 15 kV → 500 kV
• Step down at substations: 500 kV → 13.8 kV → 120 V for homes

Transformers are why AC power won over DC in the 1880s.

Key Takeaways: Electric Power Essentials

✓ — use the form that matches given variables

✓ ; energy in kWh = power (kW) × time (h)

✓ High-voltage transmission: → →

Watch Out: Avoid These Three Errors

High wattage ≠ high usefulness — a 100 W incandescent makes less light than a 15 W LED.

Higher reduces current in transmission — for fixed delivered power.

kWh is energy, not power — "500 kWh/month," not "500 kWh of power."

Chapter 19 Complete — What's Next

Chapter 20: Magnetism

• Magnetic fields: sources, field lines, force on charges
• Electromagnetic induction: changing B → EMF
• Motors, generators, transformers — the electrical grid

The analysis from today explains why transformers are essential.