The Particulate Nature of Matter - Current and Circuits

Electric Current ($I$): The rate of flow of electric charge through a conductor, defined as $I = \frac{\Delta Q}{\Delta t}$, measured in Amperes ($A$).

Microscopic Model of Current: Current depends on the particulate nature of charge carriers. It is expressed as $I = nAvq$, where $n$ is the number density of charge carriers, $A$ is the cross-sectional area, $v$ is the drift velocity, and $q$ is the elementary charge ($1.60 \times 10^{-19} C$).

Potential Difference ($V$): The work done per unit charge in moving a small positive test charge between two points, $V = \frac{W}{q}$.

Ohm's Law: For many conductors (especially metals at constant temperature), the current is proportional to the potential difference, meaning resistance $R = \frac{V}{I}$ remains constant.

Resistivity ($\rho$): A property of the material itself, independent of geometry, defined by $R = \rho \frac{L}{A}$, where $L$ is length and $A$ is cross-sectional area.

Electromotive Force (EMF, $\epsilon$): The total energy supplied by a source per unit charge. Due to internal resistance ($r$), the terminal potential difference ($V$) is often less than the EMF: $V = \epsilon - Ir$.

Kirchhoff's Laws: The Junction Law (conservation of charge) states $\sum I_{in} = \sum I_{out}$. The Loop Law (conservation of energy) states $\sum \epsilon = \sum IR$ around any closed loop.