Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Electromagnetism → Electric circuits ↓


Electric power and energy


Electricity is a fundamental part of modern life, powering everything from small household appliances to industrial machines and the grid systems that light our homes and cities. The two central concepts that underpin electrical circuits in electromagnetism are electric power and energy. Let's look at these concepts in detail, using simple examples and illustrations to clarify their meaning and importance.

Understanding electric current and voltage

Before learning about power and energy, it is necessary to understand the basic concepts of electric current and voltage, which are fundamental to understanding electrical circuits.

Electric current is the flow of electrical charge through a conductor. It is measured in amperes (A). Electric current can be thought of like the flow of water in a pipe. The greater the flow (current), the more electricity will flow.

I = Q / t

Where I is current, Q is electric charge in coulombs, and t is time in seconds.

Voltage, or electric potential difference, is the energy per charge needed to move charges from one point to another. Voltage is measured in volts (V) and is similar to water pressure in our water flow analogy.

Defining electric power

In an electrical circuit, power is the rate at which electrical energy is transferred through an electrical circuit. The basic unit of power is the watt (W), which is equal to one joule per second.

P = VI

Where P is the power in watts, V is the voltage in volts, and I is the current in amperes.

In the water flow analogy, power can be compared to the combination of water pressure and flow rate delivering water through a system.

Example

Imagine that a light bulb is connected to a circuit with a voltage of 120 volts and a current of 0.5 amperes is flowing through it. The power consumed by this bulb is:

P = VI = 120V * 0.5A = 60W

Calculation of electrical energy

While power is the rate of energy transfer, energy refers to the total amount of work done or heat generated. Energy in electrical systems is usually measured in watt-hours (Wh) or joules (J).

Electrical energy can be calculated by multiplying the power by the time it is consumed:

E = Pt

Where E is energy, P is power, and t is time in hours or seconds, depending on the unit of energy being calculated.

Example

If the same 60-watt bulb from the previous example is kept lit for 5 hours, the energy consumed can be calculated as follows:

E = Pt = 60W * 5h = 300 Wh

Resistance and power loss

In real electrical circuits, wires and other components have resistance, measured in ohms (Ω), which causes power to be lost as heat. This is described by Joule's law:

P = I²R

Where R is the resistance.

Example

A heating element with a resistance of 10 ohms is connected to a 12 volt battery. The current flowing through the element is given by Ohm's law as follows:

I = V / R = 12V / 10Ω = 1.2A

The power loss due to resistance (or power consumed in producing heat) is:

P = I²R = (1.2A)² * 10Ω = 14.4W

This example shows that resistance causes energy to be dissipated as heat, which is an important factor in the design of efficient circuits.

Visualization of power and energy concepts

To understand this better, consider an electric circuit as a loop in which a battery supplies power to a load (e.g., a bulb or resistor), as shown below:

Battery Burden

Here, the battery provides a voltage that drives current through the circuit, lighting the bulb and providing energy, which is the essence of power transfer in an electrical circuit.

Power in AC circuits

Alternating current (AC) power is used in most homes and industries. In AC circuits, power calculations become a bit more complicated because both current and voltage vary over time.

AC power can be represented as:

P(t) = V(t)I(t)

The effective power (averaged over time), particularly for sinusoidal voltages and currents, is given as:

P = VI cos(ϕ)

Where ϕ is the phase difference between voltage and current. cos(ϕ) is known as the power factor, which indicates the efficiency of power usage.

Example

For a household appliance that operates with an AC voltage of 230 volts and a current of 5 amperes with a power factor of 0.8, the actual power can be calculated as:

P = VI cos(ϕ) = 230V * 5A * 0.8 = 920W

Conversion between energy units

In practice, energy is often expressed in several different units, including joules, watt-hours, and kilowatt-hours (kWh). Converting between these units is important for understanding and comparing energy consumption.

1 watt-hour is equal to 3600 joules, because:

1 Wh = 1 W * 1 hour = 1 J/s * 3600 s = 3600 J

When dealing with larger scales, such as residential energy consumption, kilowatt-hours are typically used:

1 kWh = 1000 Wh = 3.6 x 10^6 J

Example

If an air conditioner consumes 2000 watts for 3 hours, the total energy used is:

E = Pt = 2000W * 3h = 6000 Wh = 6 kWh

Energy efficiency

An essential aspect of using electrical energy is to do so in an efficient manner. This reduces waste and conserves resources. Efficiency is defined as the ratio of useful power output to power input:

Efficiency (%) = (Useful Power Output / Power Input) x 100

For example, if an electrical appliance provides 90 watts of useful output power for 100 watts of input power, the efficiency would be:

Efficiency = (90W / 100W) x 100 = 90%

Social implications and future trends

Understanding electrical power and energy is important not only for engineering, but also for daily life. Electricity fuels our homes, industries and services. Increasing energy efficiency and developing new technologies for energy production and use are important for sustainable development.

Emerging technologies include renewable energy sources such as solar and wind power, which convert natural energy into electrical energy. Innovations also aim to improve the efficiency of electric appliances to reduce overall power consumption and its environmental impact.

As demand for electricity continues to grow, the efficient production, distribution, and use of electricity will continue to be an essential area of focus for physics, engineering, and society.

Conclusion

Electrical power and energy are fundamental concepts in the fields of electromagnetism and electrical circuits. By understanding these concepts, we can efficiently use electricity to power the myriad devices and systems that define modern life. Whether through calculations involving P = VI or analyzing power factor in AC circuits, mastering these ideas is important for anyone studying physics or working with electrical systems.


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