Current Electricity — Core Principles

Core Principles

Current electricity deals with the flow of electric charge, known as electric current, through conductors. This flow is driven by a potential difference (voltage) and is opposed by resistance. Ohm's Law ($V=IR$) describes the fundamental relationship between voltage, current, and resistance.

Resistance depends on the material's intrinsic property called resistivity, its length, and cross-sectional area. Conductors have low resistance, while insulators have high resistance. For complex circuits, Kirchhoff's Laws are essential: KCL (Junction Rule) states that charge is conserved at any junction, and KVL (Loop Rule) states that energy is conserved around any closed loop.

EMF represents the total potential provided by a source, while internal resistance causes a drop in terminal voltage when current is drawn. Devices like the Wheatstone bridge, Meter bridge, and Potentiometer are used for precise resistance and potential difference measurements.

The flow of current also produces heat (Joule's Law) and delivers power, which are crucial for various applications.

Important Differences

vs Potential Difference (Terminal Voltage)

Aspect	This Topic	Potential Difference (Terminal Voltage)
Definition	Electromotive Force (EMF, $mathcal{E}$): The work done by the source per unit charge to move charge from its lower potential terminal to its higher potential terminal within the source itself, in an open circuit (no current drawn). It represents the total energy supplied by the source.	Potential Difference (Terminal Voltage, $V$): The work done per unit charge in moving a charge between two points in an electric field. Specifically, the voltage measured across the terminals of a source when current is being drawn from it.
Measurement	Measured when no current is drawn from the source (open circuit). A potentiometer can measure EMF accurately.	Measured when current is flowing through the external circuit. A voltmeter measures terminal potential difference.
Relation to Internal Resistance	Independent of the internal resistance of the source, as it's the inherent property of the source to generate potential.	Dependent on the internal resistance ($r$) and the current ($I$) drawn: $V = mathcal{E} - Ir$. It is always less than or equal to EMF (equal only when $I=0$). If charging, $V = mathcal{E} + Ir$.
Cause/Effect	The 'cause' that drives the current in a circuit.	The 'effect' or the actual voltage available to the external circuit.
Value	Maximum potential difference provided by the source.	Always less than or equal to EMF (when discharging), or greater than EMF (when charging).

EMF is the inherent potential-generating capacity of a source, measured in an open circuit, representing the total energy per unit charge. Potential difference, or terminal voltage, is the actual voltage available across the terminals of the source when current is flowing, which is always less than the EMF due to the voltage drop across the source's internal resistance. EMF is the cause, while terminal voltage is the effect observed in a working circuit. A potentiometer measures EMF accurately without drawing current, whereas a voltmeter measures terminal potential difference.