2.1 Charge, current, voltage, and power

Charge, current, voltage, and power are the building blocks of electrical systems. They describe how electricity moves and works in circuits. Understanding these concepts is crucial for grasping how electrical devices function and interact.

These fundamental quantities are interconnected through key relationships like Ohm's Law. Mastering them sets the foundation for analyzing more complex electrical systems and solving real-world engineering problems.

Charge and Current

Electric Charge and the Coulomb

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• Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field
• Charges can be positive or negative, with opposite charges attracting and like charges repelling each other
• The unit of electric charge is the coulomb (C), named after Charles-Augustin de Coulomb
  • One coulomb is defined as the amount of charge transferred by a current of one ampere in one second ($1C = 1A \cdot 1s$)
  • The charge of an electron is approximately $-1.602 \times 10^{-19}$ coulombs, while a proton has a charge of $+1.602 \times 10^{-19}$ coulombs

Current and the Ampere

• Current is the flow of electric charge through a material, typically measured in amperes (A)
  • One ampere is defined as the flow of one coulomb of charge per second ($1A = 1C/s$)
• Current can be either direct current (DC) or alternating current (AC)
  • DC flows in one direction consistently, like in a battery-powered circuit
  • AC periodically reverses direction, like in household electrical outlets
• The direction of conventional current is defined as the direction in which positive charges would flow, from the positive terminal to the negative terminal
  • However, in most materials, electric current is actually carried by negatively charged electrons moving in the opposite direction

Voltage and Electric Fields

Voltage and the Volt

• Voltage, also known as electromotive force (EMF), is the difference in electric potential energy per unit charge between two points in an electrical circuit
• The unit of voltage is the volt (V), named after Alessandro Volta
  • One volt is defined as the potential difference between two points in a conductor when a current of one ampere dissipates one watt of power ($1V = 1W/A$)
• Voltage can be thought of as the "pressure" that pushes electric charges through a circuit
  • A higher voltage means a greater potential difference and a stronger "push" on the charges

Electric Fields and Potential Difference

• An electric field is a region around an electrically charged particle or object in which another charged particle experiences a force
• The strength of an electric field is measured in volts per meter (V/m)
  • A potential difference of one volt between two points one meter apart creates an electric field strength of one volt per meter
• The relationship between voltage and electric field strength is given by $V = Ed$, where $V$ is the voltage, $E$ is the electric field strength, and $d$ is the distance between the two points
• Electric fields can be visualized using field lines, which point in the direction a positive test charge would move if placed in the field
  • Field lines start on positive charges and end on negative charges, with the density of lines indicating the strength of the field

Power and Ohm's Law

Power and the Watt

• Power is the rate at which energy is transferred or converted, measured in watts (W)
  • One watt is defined as one joule of energy per second ($1W = 1J/s$)
• In electrical systems, power is the product of voltage and current, given by the formula [P = VI](https://www.fiveableKeyTerm:p_=_vi), where $P$ is power, $V$ is voltage, and $I$ is current
  • For example, a 12V battery supplying 5A of current is providing $12V \times 5A = 60W$ of power
• Power can also be expressed in terms of resistance and either voltage or current: $P = V^2/R$ or $P = I^2R$, where $R$ is resistance in ohms

Ohm's Law

• Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant
• Mathematically, Ohm's Law is expressed as $V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance
  • Rearranging this equation gives $I = V/R$ and $R = V/I$, allowing you to calculate any of the three quantities given the other two
• Resistance is measured in ohms ($\Omega$), named after Georg Ohm
  • One ohm is defined as the resistance between two points in a conductor where a voltage of one volt produces a current of one ampere ($1\Omega = 1V/A$)
• Ohm's Law is a fundamental principle in electrical engineering and is used to analyze and design electrical circuits
  • For instance, if a 10$\Omega$ resistor is connected across a 5V battery, Ohm's Law tells us that the current through the resistor will be $I = V/R = 5V/10\Omega = 0.5A$