9.5 Electrical Energy and Power

Electrical energy and power are crucial concepts in understanding how electricity works and is used. They explain how energy flows through circuits, gets converted into other forms, and impacts our daily lives through various devices and appliances.

Voltage, current, and resistance play key roles in determining power and energy consumption. Understanding these relationships helps us analyze circuit behavior, calculate energy costs, and improve the efficiency of electrical systems in our homes and industries.

Electrical Energy and Power

Voltage and current in power

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• Power ($P$) represents rate electrical energy converts into other forms (heat, mechanical work)
• Measured in watts ($W$)
• Calculated by multiplying voltage ($V$) and current ($I$): $P = VI$
  • Voltage measured in volts ($V$)
  • Current measured in amperes ($A$)
• For resistors, power also expressed using Ohm's law: $P = I^2R$ or $P = \frac{V^2}{R}$
  • $R$ represents resistance, measured in ohms ($\Omega$)
• Examples:
  • Electric heater (1500 W) operating at 120 V draws 12.5 A of current
  • Lightbulb (60 W) with 120 V supply has 0.5 A current flowing through it

Power dissipation in resistors

• Resistors convert electrical energy into heat through Joule heating
• Power dissipated equals voltage across resistor multiplied by current through it: $P = VI$
• In series circuits, total power dissipated equals sum of power dissipated by each resistor: $P_{total} = P_1 + P_2 + ... + P_n$
• Parallel circuits have total power dissipated equal to sum of power dissipated by each branch: $P_{total} = P_1 + P_2 + ... + P_n$
• Total power supplied by voltage source equals sum of power dissipated by all circuit components
• Examples:
  • Two 100 $\Omega$ resistors in series with 10 V supply dissipate 0.5 W each, totaling 1 W
  • Three 300 $\Omega$ resistors in parallel with 12 V supply dissipate 0.16 W each, totaling 0.48 W

Energy efficiency of electrical devices

• Electrical energy measured in joules ($J$) or kilowatt-hours ($kWh$)
  • $1 kWh = 3.6 \times 10^6 J$
• Energy consumed by device equals its power multiplied by usage time: $E = Pt$
  • $E$ represents energy in joules ($J$)
  • $P$ represents power in watts ($W$)
  • $t$ represents time in seconds ($s$)
• Energy efficiency is ratio of useful output energy to input energy, often a percentage
  • Higher efficiency means less energy wasted as heat or other forms
• Cost-effectiveness compares operating cost to energy efficiency and performance
  • Electricity cost typically in cents per kilowatt-hour ($\cent/kWh$)
  • Operating cost calculated by multiplying power, usage time, and cost per kilowatt-hour: $Cost = P \times t \times (\cent/kWh)$
• Examples:
  • LED bulb (9 W) produces same light as 60 W incandescent bulb, 85% more efficient
  • Refrigerator (400 kWh/year) at $0.12/kWh costs$48 annually to operate

Electric fields and potential

• Electric field represents the force per unit charge exerted on a charged particle in space
• Electric potential is the potential energy per unit charge at a point in an electric field
• Conductors allow easy flow of electric charge, while insulators impede charge flow
• Electromotive force (EMF) is the energy per unit charge supplied by a source in a circuit
• Capacitance measures a device's ability to store electric charge, affecting circuit behavior

Alternating current

• Alternating current (AC) periodically reverses direction, unlike direct current (DC)
• AC is commonly used in household electrical systems and power distribution