1: Charge, current, voltage, power, energy

Section 1: Basic Concepts - Charge, Current, Voltage, Power, Energy

Understanding these five fundamental quantities is essential for analyzing any electrical circuit.

1. Charge (Q): Electric charge is a fundamental property of matter carried by particles like electrons (negative charge) and protons (positive charge). It is measured in Coulombs (C). One Coulomb equals the charge of approximately $6.242 \times 10^{18}$ electrons. Charge is conserved in an isolated system.

2. Current (I): Electric current is the rate of flow of electric charge past a given point in a circuit. It is defined mathematically as:
   $I = dQ/dt$
   where $I$ is current in Amperes (A), $dQ$ is the small change in charge in Coulombs (C), and $dt$ is the small change in time in seconds (s). One Ampere equals one Coulomb flowing per second. Current flows from a point of higher electric potential (positive terminal) to lower potential (negative terminal) in the external circuit (conventional current flow), opposite to the direction of electron drift.

3. Voltage (V) / Potential Difference / Electromotive Force (EMF): Voltage, or potential difference, is the energy required to move a unit charge between two points in an electric field. It is the driving force that causes charge to flow (current). It is defined as:
   $V = dW/dQ$
   where $V$ is voltage in Volts (V), $dW$ is the small change in energy in Joules (J), and $dQ$ is the small change in charge in Coulombs (C). One Volt equals one Joule per Coulomb. A voltage source (like a battery or generator) provides Electromotive Force (EMF), which is the voltage it produces when no current is flowing. Voltage is always measured between two points.

4. Power (P): Electrical power is the rate at which electrical energy is transferred or consumed by a component in a circuit. It is defined as:
   $P = dW/dt$
   where $P$ is power in Watts (W) and $dW/dt$ is the rate of energy transfer in Joules per second (J/s). Using the definitions of voltage and current, power can be expressed as:
   $P = V \cdot I$
   For resistive elements (obeying Ohm's Law, $V = I \cdot R$), power can also be calculated as:
   $P = I^{2} \cdot R$ or $P = V^{2}/R$

5. Energy (W): Electrical energy is the capacity to do work resulting from the movement of charge driven by voltage over a period of time. It is measured in Joules (J). Energy is the total work done or heat generated. It is calculated by integrating power over time:
   $W = \int P dt$
   For constant power, this simplifies to:
   $W = P \cdot t$
   where $t$ is time in seconds (s). In practical terms, energy supplied by utilities is often measured in kilowatt-hours (kWh), where 1 kWh $= 3.6 \times 10^{6}$ J.