Electromotive force (EMF), denoted by ε (epsilon), is NOT actually a force — it is a potential difference (measured in Volts). EMF is defined as the work done by the battery per unit charge in driving the charge through the complete circuit, including through the battery itself. In simpler terms, EMF is the maximum voltage a battery can provide when no current is being drawn from it (open circuit condition).

EMF arises from the conversion of some other form of energy (chemical, mechanical, solar, etc.) into electrical energy inside the source. In a chemical battery, the chemical reactions between the electrodes and the electrolyte create a potential difference that drives the current. The EMF of a cell depends on the nature of the electrolyte and electrode material, not on the size or shape of the cell.

Every real battery or cell has some resistance to the flow of current within itself, called internal resistance (r). This arises from the resistance of the electrolyte and the electrodes inside the cell. Even though we cannot see it externally, internal resistance behaves exactly like a series resistor connected inside the battery.

As a battery gets older or discharged, its internal resistance increases. A freshly charged battery has low internal resistance, allowing it to deliver higher current. When a battery "dies," it often still has some EMF remaining, but its internal resistance has increased so much that the terminal voltage drops significantly under load.

Terminal voltage (V) is the actual voltage available at the terminals of the battery when current is flowing. It is always different from EMF when current flows, because of the voltage drop across the internal resistance.

This is the single most important set of formulas for this topic in NEET. Memorise all three cases:

The terminal voltage formula can also be derived using Kirchhoff's Voltage Law (KVL). Going around the circuit loop: EMF − voltage drop across internal resistance − voltage across external resistance = 0. This gives ε − Ir − IR = 0, so IR = ε − Ir. Since IR = V (terminal voltage), we get V = ε − Ir.

The current in the circuit can also be written as:

where R is the external resistance and r is the internal resistance. This is the most fundamental equation for a circuit with a real battery.

The total power delivered by the EMF source is P_total = εI. This total power is split between the external circuit and the internal resistance. Power delivered to external circuit: P_external = I²R = VI. Power lost inside battery: P_internal = I²r. Conservation of energy gives: εI = I²R + I²r, or ε = IR + Ir, which is consistent with our KVL equation.

The efficiency of the battery (ratio of useful power to total power) is:

For maximum efficiency, R >> r. For maximum power transfer (different from efficiency), R = r — this is the condition of maximum power transfer theorem.

In NEET, problems on grouping of cells are very common. For n cells each of EMF ε and internal resistance r:

Series grouping is preferred when external resistance is large. Parallel grouping is preferred when external resistance is small (to match internal resistance for better efficiency). Mixed grouping gives maximum current when R = nr/m (internal = external resistance condition).

A potentiometer is used to measure the exact EMF of a cell without drawing any current, because at balance point the galvanometer shows zero deflection meaning no current flows through the cell branch. Since I = 0, V = ε exactly. A voltmeter, on the other hand, always draws a small current and hence reads terminal voltage slightly less than EMF.

To find internal resistance experimentally: measure terminal voltage V with external resistance R. Then r = (ε − V)/I = (ε − V)R/V. This can be rearranged to give a straight line equation, allowing r to be found from a graph of V vs I.