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 's law: P=I2R or P=RV2
R represents resistance, measured in ohms (Ω)
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=VI
In series circuits, total power dissipated equals sum of power dissipated by each : Ptotal=P1+P2+...+Pn
Parallel circuits have total power dissipated equal to sum of power dissipated by each branch: Ptotal=P1+P2+...+Pn
Total power supplied by voltage source equals sum of power dissipated by all circuit components
Examples:
Two 100 Ω resistors in series with 10 V supply dissipate 0.5 W each, totaling 1 W
Three 300 Ω 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)
1kWh=3.6×106J
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)
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)
Operating cost calculated by multiplying power, usage time, and cost per kilowatt-hour: Cost=P×t×(\cent/kWh)
Examples:
bulb (9 W) produces same light as 60 W , 85% more efficient
Refrigerator (400 kWh/year) at 0.12/kWhcosts48 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