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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 (PP) represents rate electrical energy converts into other forms (heat, mechanical work)
  • Measured in watts (WW)
  • Calculated by multiplying voltage (VV) and current (II): P=VIP = VI
    • Voltage measured in volts (VV)
    • Current measured in amperes (AA)
  • For resistors, power also expressed using 's law: P=I2RP = I^2R or P=V2RP = \frac{V^2}{R}
    • RR represents resistance, measured in ohms (Ω\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
  • Power dissipated equals voltage across multiplied by current through it: P=VIP = VI
  • In series circuits, total power dissipated equals sum of power dissipated by each : Ptotal=P1+P2+...+PnP_{total} = P_1 + P_2 + ... + P_n
  • Parallel circuits have total power dissipated equal to sum of power dissipated by each branch: Ptotal=P1+P2+...+PnP_{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 Ω\Omega resistors in series with 10 V supply dissipate 0.5 W each, totaling 1 W
    • Three 300 Ω\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 (JJ) or kilowatt-hours (kWhkWh)
    • 1kWh=3.6×106J1 kWh = 3.6 \times 10^6 J
  • Energy consumed by device equals its power multiplied by usage time: E=PtE = Pt
    • EE represents energy in joules (JJ)
    • PP represents power in watts (WW)
    • tt represents time in seconds (ss)
  • 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 (\cent/kWh\cent/kWh)
    • Operating cost calculated by multiplying power, usage time, and cost per kilowatt-hour: Cost=P×t×(\cent/kWh)Cost = P \times t \times (\cent/kWh)
  • Examples:
    • bulb (9 W) produces same light as 60 W , 85% more efficient
    • Refrigerator (400 kWh/year) at 0.12/kWhcosts0.12/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
  • is the potential energy per unit charge at a point in an electric field
  • allow easy flow of electric charge, while impede charge flow
  • (EMF) is the energy per unit charge supplied by a source in a circuit
  • measures a device's ability to store electric charge, affecting circuit behavior

Alternating current

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

Key Terms to Review (20)

Alternating Current: Alternating current (AC) is an electric current that periodically reverses direction, in contrast to direct current (DC) which flows in a constant direction. AC is the standard form of electricity distribution and is used in a wide range of applications, from powering household appliances to generating electricity in power plants.
Alternating current (ac): Alternating current (AC) is an electric current that periodically reverses direction. Unlike direct current (DC), AC voltage and current change their magnitudes continuously with time.
Capacitance: Capacitance is the ability of a system to store charge per unit voltage. It is measured in farads (F).
Capacitance: Capacitance is a measure of the ability of a capacitor to store electric charge. It is a fundamental quantity in the study of electricity and electronics, and it plays a crucial role in various topics related to electrostatic equilibrium, electric potential, and energy storage.
Conductors: Conductors are materials that allow the flow of electric current with minimal resistance. They facilitate the movement of charge carriers, such as electrons, making them essential for the operation of electrical circuits, devices, and systems that rely on the efficient transfer of electrical energy.
Electric potential: Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. It is measured in volts (V).
Electric Potential: Electric potential, also known as electrostatic potential, is a scalar quantity that represents the amount of work done per unit charge in moving a test charge from an infinite distance to a specific point in an electric field. It is a measure of the potential energy per unit charge at a given location within an electric field.
Electric power: Electric power is the rate at which electrical energy is transferred by an electric circuit. It is typically measured in watts (W), where 1 watt equals 1 joule per second.
Electrical Energy: Electrical energy is the energy associated with the movement of electric charge, such as electrons, through a conductor like a wire. It is the form of energy generated, transmitted, and used to power various devices and systems in our daily lives.
Electromotive Force: Electromotive force (EMF) is the voltage or potential difference generated in an electrical circuit, typically by a source of electrical energy such as a battery or generator. It is the driving force that causes electric charge to flow through a circuit, enabling the conversion of other forms of energy into electrical energy.
Energy Efficiency: Energy efficiency refers to the ability to accomplish a given task with the least amount of energy input. It is a measure of how effectively energy is utilized to perform work or provide a desired output, rather than being wasted or lost as heat or other forms of energy.
Incandescent Bulb: An incandescent bulb is a type of electric lamp that produces light by heating a thin wire filament to a high temperature using an electric current. The heated filament emits visible light through the process of incandescence, which is the emission of light due to the thermal energy of the material.
Insulators: Insulators are materials that have a very high resistance to the flow of electric current, effectively preventing the passage of electric charges. They are essential in the context of electrical energy and power as they help control and direct the flow of electricity.
Joule Heating: Joule heating, also known as resistive heating, is the process by which the passage of an electric current through a conductor generates heat. This heating effect is caused by the collisions of the moving electrons with the atoms in the conductor, which results in the conversion of electrical energy into thermal energy.
Kilowatt-hour: A kilowatt-hour (kWh) is a unit of measurement that represents the amount of electrical energy consumed or generated over a period of time. It is the product of power in kilowatts (kW) and time in hours (h), providing a way to quantify the energy usage or production of electrical devices and systems.
LED: LED stands for Light-Emitting Diode, which is a semiconductor device that emits light when an electric current is applied. LEDs are widely used in various applications, including lighting, displays, and signaling, due to their energy efficiency, long lifespan, and versatility.
Nonohmic: A nonohmic material is one whose resistance does not remain constant as the voltage or current changes. This means it does not follow Ohm's Law, where $V = IR$.
Ohm: Ohm is the fundamental unit of electrical resistance, named after the German physicist Georg Ohm. It represents the amount of resistance that an electrical circuit or component offers to the flow of electric current, and is a crucial concept in understanding the behavior of electrical systems.
Resistor: A resistor is a passive electrical component that opposes the flow of electric current, resulting in a drop in voltage. It is characterized by its resistance, measured in ohms ($\Omega$).
Resistor: A resistor is a passive electronic component that is used to control or limit the flow of electric current in a circuit. It is a fundamental building block of electrical and electronic systems, playing a crucial role in the context of resistivity, resistance, electrical energy, and power.
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Glossary
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9.6 Superconductors