Talha's Physics Academy
Electromotive Force and Internal Resistance
Video Lecture
Watch the complete video lecture below to understand electromotive force (EMF), internal resistance, and terminal potential difference derivations.
Electromotive Force (E.M.F)
Electromotive force is denoted by the symbol $E$ (or $\mathcal{E}$). Energy conversion takes place in sources of EMF:
- In a battery, chemical energy is converted into electrical energy.
- In a generator, mechanical energy is converted into electrical energy.
- In a thermocouple, heat energy is converted into electrical energy.
Internal Resistance
Consider a circuit in which an external resistor $R$ is connected by leads of negligible resistance across the terminals of a battery. When a current $I$ flows through the circuit from the negative terminal to the positive terminal inside the battery, it encounters opposition due to the electrolyte and electrodes present within the source. This inherent opposition is known as the internal resistance ($r$) of the battery.
Derivation of the Relation Between EMF, Terminal Voltage, and Internal Resistance
According to Ohm's Law, the total current $I$ flowing through the complete circuit (total resistance $R + r$) is given by:
$$I = \frac{E}{R + r}$$
Rearranging this equation yields:
$$E = I(R + r)$$
$$E = IR + Ir \quad \text{--- (i)}$$
Where:
- $IR = V$ is the terminal potential difference across the external resistor $R$.
- $Ir$ is the lost voltage (potential drop) across the internal resistance $r$ of the battery.
Substituting $V = IR$ into equation (i):
$$E = V + Ir$$
$$V = E - Ir$$
Key Insight: This equation shows that the terminal potential difference $V$ drops below the EMF $E$ by an amount equal to $Ir$ when the battery delivers a current. However, when no current is drawn ($I = 0$), there is no potential drop across the internal resistance, making the terminal potential difference exactly equal to the source EMF ($V = E$).
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