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, whereas terminal p.d. is the energy delivered to the external circuit per unit charge. The difference between them is the energy lost per unit charge (lost volts) due to internal resistance.

How does an 'ideal' power supply differ from a 'real' power supply in terms of internal resistance?

An ideal power supply is modeled with zero internal resistance, meaning its terminal p.d. remains constant regardless of the current. A real power supply has a non-zero internal resistance that causes the terminal p.d. to drop as the current increases.

When is the terminal potential difference of a cell exactly equal to its e.m.f.?

This occurs only when no current is flowing through the circuit (an open circuit). When $I = 0$, the 'lost volts' ($Ir$) becomes zero, making the terminal p.d. ($V = \epsilon - Ir$) equal to the e.m.f. ($\epsilon$).

What is a common error when calculating the power delivered to a load from a real battery?

A common error is using the e.m.f. value instead of the terminal potential difference in the power formula $P = VI$. Using e.m.f. calculates the total power generated, not the power actually received by the external load.

Why is it incorrect to assume the gradient of a $V-I$ graph for a battery is positive?

The gradient must be negative because as current increases, the 'lost volts' ($Ir$) also increase, which reduces the terminal voltage ($V$). Mathematically, $V = -rI + \epsilon$, where $-r$ is the negative gradient.

What mistake is made if a student ignores internal resistance in a high-current circuit?

In high-current circuits, the 'lost volts' ($Ir$) become significant. Ignoring $r$ leads to an overestimation of the voltage available to components, which can result in incorrect predictions of component behavior or brightness.

Define 'Lost Volts' in the context of a DC circuit.

Lost volts refers to the potential difference that is dropped across the internal resistance of a power source. It represents the energy per unit charge that is converted into heat within the battery rather than being useful in the external circuit.

State the full e.m.f. equation relating current, load resistance, and internal resistance.

The equation is $\epsilon = I(R + r)$, where $\epsilon$ is the e.m.f., $I$ is the circuit current, $R$ is the external load resistance, and $r$ is the internal resistance. This shows that the total e.m.f. is used across both the external and internal parts of the circuit.

How can you determine the e.m.f. of a cell from a graph of Terminal P.D. ($V$) against Current ($I$)?

The e.m.f. is found by identifying the y-intercept of the graph. This point represents the voltage when the current is zero, which by definition is the electromotive force of the source.

Why does a battery become warm when it is used to power a high-current device for a long time?

As current flows through the internal resistance of the battery, electrical energy is converted into thermal energy due to the $P = I^2r$ relationship. This internal heating is a direct consequence of the work done to move charge against the internal resistance.

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Internal Resistance

Summary

Internal resistance is the inherent opposition to the flow of current within a power source itself, such as a battery or cell. It results in a portion of the source's total energy (e.m.f.) being dissipated as heat internally, which reduces the voltage available to the external circuit as the current increases.

1. Definition & Core Concepts

Internal Resistance ( $r$ ): This is the resistance found inside a power supply between its terminals, caused by the chemical and physical properties of the materials within the cell.
Electromotive Force (e.m.f. or $\epsilon$ ): The total energy converted from other forms (like chemical) into electrical energy per unit charge when charge passes through the power supply.
Terminal Potential Difference ( $V$ ): The actual voltage measured across the terminals of the power supply when it is connected to a circuit and current is flowing.
Lost Volts ( $V_{lost}$ ): The potential difference dropped across the internal resistance of the cell, calculated as $V_{lost} = I \cdot r$ .

Circuit diagram showing a real cell modeled as an ideal e.m.f. source in series with an internal resistor r, connected to an external load resistor R.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions