What is the fundamental difference between E.M.F. and Terminal Potential Difference?

E.M.F. is the total energy supplied by the source per unit charge, while Terminal PD is the energy delivered to the external circuit. The difference is due to the energy dissipated by the source's internal resistance.

Under what specific condition does the Terminal Potential Difference equal the E.M.F.?

This occurs only when no current is flowing through the circuit (open circuit condition, $I = 0$) or if the source is 'ideal' with zero internal resistance ($r = 0$). In these cases, there is no voltage drop across the internal resistance.

How does the Terminal Potential Difference change when a cell is being charged instead of discharging?

During charging, current is forced into the positive terminal, reversing the internal voltage drop. The relationship becomes $V = \epsilon + Ir$, meaning the terminal voltage must be greater than the E.M.F. to overcome the internal resistance.

Why is it incorrect to assume that the voltage across a battery's terminals is constant?

The terminal voltage depends on the current being drawn. As the load increases (lower resistance), the current rises, which increases the 'lost volts' ($Ir$) across the internal resistance, thereby reducing the terminal voltage.

What is the 'lost volts' misconception regarding energy conservation?

Students often think 'lost volts' are simply gone; however, they represent energy converted into heat within the battery. It is not a violation of energy conservation but a conversion into an unusable form (thermal energy).

Why can a standard voltmeter never measure the exact E.M.F. of a real battery?

A voltmeter requires a small amount of current to operate. This current causes a small voltage drop across the battery's internal resistance, meaning the voltmeter always measures the terminal voltage ($V$) rather than the true E.M.F. ($\epsilon$).

Define 'Internal Resistance' in the context of an electric cell.

Internal resistance is the opposition to the flow of current offered by the materials (electrolytes and electrodes) inside the cell itself. It results in the generation of heat and a reduction in terminal voltage when current flows.

What is the formula for the current in a circuit containing a source with internal resistance?

The current is given by $I = \frac{\epsilon}{R + r}$, where $\epsilon$ is the E.M.F., $R$ is the external load resistance, and $r$ is the internal resistance. This treats the internal and external resistances as being in series.

State the relationship between Terminal PD, E.M.F., and internal resistance for a discharging source.

The relationship is $V = \epsilon - Ir$. Here, $V$ is the terminal potential difference, $\epsilon$ is the electromotive force, $I$ is the current, and $r$ is the internal resistance.

Why does a battery get warm when it is used to power a high-current device?

The high current flowing through the battery's internal resistance ($r$) generates heat according to the formula $P = I^2r$. This thermal energy is the physical manifestation of the 'lost volts' in the circuit.

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E.M.F. vs. Terminal Potential Difference

Summary

This topic explores the distinction between the total energy supplied by an electrical source (Electromotive Force) and the actual energy delivered to an external circuit (Terminal Potential Difference). The discrepancy between these two values is fundamentally caused by the internal resistance of the source, which dissipates energy as heat within the source itself whenever a current flows.

1. Definition & Core Concepts

Electromotive Force (E.M.F., $\epsilon$ ): This is defined as the total work done by a source (like a battery or generator) in moving a unit positive charge through a complete circuit, including the source itself. It represents the maximum potential difference the source can provide when no current is being drawn (open circuit).
Terminal Potential Difference (V): This is the potential difference across the terminals of a source when it is supplying current to an external circuit. It represents the energy delivered to the external components per unit charge.
Internal Resistance (r): Every real-world electrical source possesses an inherent resistance to the flow of charge within itself. This resistance causes a portion of the source's energy to be converted into heat before the charge even leaves the source.

Circuit diagram showing a source with E.M.F. (ε) and internal resistance (r) connected to an external load (R), highlighting the difference between internal and terminal voltage.

2. Underlying Principles

3. Mathematical Framework

4. Key Distinctions

5. Measurement Techniques

Voltmeter Limitations: A standard voltmeter has high but finite resistance. When connected across a source, it draws a small current, meaning it actually measures Terminal Potential Difference ( $V$ ) rather than true E.M.F. ( $\epsilon$ ).
Potentiometer Advantage: A potentiometer is an ideal instrument for measuring E.M.F. because it operates on a 'null method' where no current is drawn from the source at the point of balance. This allows for the measurement of $\epsilon$ without the interference of internal resistance.
Open Circuit Condition: In theory, E.M.F. is the reading of an ideal voltmeter (infinite resistance) connected across the terminals of a source when no other load is connected.

6. Exam Strategy & Common Pitfalls