Electric power and energy are crucial concepts in understanding how electricity works in our daily lives. They explain how devices use electricity and how we measure and pay for it.

Power tells us how quickly energy is used, while electrical energy measures the total amount consumed over time. These ideas help us calculate electricity costs and understand how different appliances affect our energy bills.

Electric Power and Energy

Power dissipation in electric circuits

• Power ($P$) represents the rate of energy transfer or conversion measured in watts ($W$) where $1 \text{ watt} = 1 \text{ joule per second} \text{ (J/s)}$
• Power dissipated by a resistor can be calculated using three formulas:
  • $P = IV$ multiplies current ($I$) and voltage ($V$) across the resistor (light bulb)
  • $P = I^2R$ squares current ($I$) and multiplies by resistance ($R$) (heating element)
  • $P = \frac{V^2}{R}$ squares voltage ($V$) and divides by resistance ($R$) (electric motor)
• Power supplied by a source is calculated as $P = IV$ multiplying current ($I$) and voltage ($V$) of the source (battery)
• Conservation of energy principle states that total power supplied by sources must equal total power dissipated by resistors in a circuit (power balance)

Electricity costs of household devices

• Electrical energy is measured in kilowatt-hours (kWh) where $1 \text{ kWh} = 1000 \text{ watts} \times 1 \text{ hour} = 3.6 \times 10^6 \text{ joules}$
• Energy consumption is calculated as $\text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (hours)}$
• Electricity cost is determined by multiplying energy consumption (kWh) and price per kWh which varies by location and provider
• To estimate costs:
  1. Determine the power rating of the appliance or device in watts (60W light bulb)
  2. Estimate the average daily use time in hours (4 hours per day)
  3. Convert power to kilowatts and multiply by daily use time to get daily energy consumption (0.24 kWh per day)
  4. Multiply daily energy consumption by the price per kWh to estimate daily cost ($0.12 per kWh results in $0.029 per day)

Relationships in DC circuit components

• Ohm's Law states that voltage ($V$) is directly proportional to current ($I$) and resistance ($R$) expressed as $V = IR$
  • Increasing voltage increases current if resistance is constant (higher battery voltage)
  • Increasing resistance decreases current if voltage is constant (dimmer switch)
• Power relationships in DC circuits:
  • $P = IV$ shows power is directly proportional to both current and voltage doubling either doubles power if the other is constant (brighter bulb)
  • $P = I^2R$ shows power is directly proportional to resistance and the square of current doubling current quadruples power if resistance is constant (faster motor)
  • $P = \frac{V^2}{R}$ shows power is directly proportional to the square of voltage and inversely proportional to resistance doubling voltage quadruples power if resistance is constant (hotter heater)
• The potential difference between two points in a circuit drives the flow of electric current through the electric field

Additional Electrical Concepts

• Electrical conductivity is a measure of a material's ability to conduct electric current, affecting the resistance in a circuit
• Electromotive force (emf) is the energy per unit charge supplied by a source in a circuit, such as a battery
• Alternating current (AC) is a type of electric current that periodically reverses direction, commonly used in household electricity supply