Cells, EMF, Internal Resistance — Core Principles

Core Principles

A cell is a source of electromotive force (EMF), $E$, which represents the maximum potential difference it can provide. This EMF is generated by chemical reactions within the cell, converting chemical energy into electrical energy.

All real cells possess an internal resistance, $r$, due to the materials and processes inside them. When a current $I$ is drawn from the cell, a voltage drop $Ir$ occurs across this internal resistance.

Consequently, the actual voltage available at the cell's terminals, known as the terminal potential difference $V$, is less than the EMF. This relationship is given by $V = E - Ir$. If the cell is on an open circuit (no current), $V=E$.

If the cell is being charged, $V = E + Ir$. Cells can be combined in series to increase the total EMF ($E_{eq} = nE$, $r_{eq} = nr$) or in parallel to increase current capacity and reduce equivalent internal resistance ($E_{eq} = E$, $r_{eq} = r/n$ for identical cells).

Understanding these concepts is fundamental to analyzing real-world electrical circuits.

Important Differences

vs Terminal Potential Difference

Aspect	This Topic	Terminal Potential Difference
Definition	Electromotive Force (EMF)	Terminal Potential Difference (V)
Definition	The maximum potential difference across the cell's terminals when no current is drawn (open circuit). It's the work done by the cell per unit charge.	The actual potential difference across the cell's terminals when current is being drawn from or supplied to the cell (closed circuit).
Symbol	$E$	$V$
Measurement	Measured by a potentiometer or a high-resistance voltmeter in an open circuit.	Measured by a voltmeter connected across the terminals in a closed circuit.
Relationship	Intrinsic property of the cell, constant for a given cell (under ideal conditions).	Varies with the current drawn from the cell: $V = E - Ir$ (discharging) or $V = E + Ir$ (charging).
Value Comparison	Always greater than or equal to the terminal potential difference ($E ge V$).	Always less than or equal to the EMF ($V le E$) when discharging, but can be greater than EMF when charging ($V > E$). If $I=0$, then $V=E$.
Cause	Chemical reactions within the cell.	Potential drop across the external resistance, influenced by internal resistance.

EMF is the inherent 'push' a cell can provide, representing its maximum potential difference under no-load conditions. It's a constant value for a given cell. Terminal potential difference, on the other hand, is the actual voltage measured across the cell's terminals when it's actively supplying current to a circuit. This value is always less than the EMF during discharge due to the voltage drop across the cell's internal resistance ($Ir$). The only time they are equal is when no current flows, or the cell is on an open circuit. Understanding this distinction is vital for accurate circuit analysis.