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

E.M.F. is the total energy supplied per unit charge by the source (measured at zero current), while Terminal PD is the energy per unit charge delivered to the external circuit (measured when current flows). The difference between them is the 'lost volts' ($Ir$).

How does an ideal power source differ from a real power source regarding internal resistance?

An ideal power source has zero internal resistance ($r = 0$), meaning its terminal PD always equals its E.M.F. regardless of the current. A real power source has a non-zero internal resistance that causes the terminal PD to drop as current increases.

When is the terminal potential difference of a cell equal to its E.M.F.?

This occurs only when no current is flowing through the circuit (an 'open circuit' condition). In this state, the 'lost volts' ($Ir$) term becomes zero, so $V = \epsilon - 0 = \epsilon$.

What error occurs if the switch is left closed for long periods during the experiment?

The cell will heat up due to the current flowing through its internal resistance. Since resistance often changes with temperature, the internal resistance ($r$) will not remain constant, leading to a non-linear $V-I$ graph and inaccurate results.

What is a common mistake when interpreting the gradient of a $V$ vs $I$ graph?

Students often forget that the gradient is negative ($-r$). While the mathematical slope is negative, the physical property of resistance is expressed as a positive value, so the internal resistance is the absolute value of the gradient.

Why might a calculated E.M.F. be lower than expected if using an old voltmeter?

If the voltmeter has a relatively low resistance, it acts as a parallel load and draws a small current even when the rest of the circuit is open. This creates 'lost volts' within the cell, causing the measured voltage to be less than the true E.M.F.

Define 'Internal Resistance' in the context of a chemical cell.

Internal resistance is the opposition to the flow of charge within the cell itself, arising from the resistance of the electrolyte and the electrodes. It results in a potential drop when the cell supplies current.

What is the formula relating E.M.F., Terminal PD, Current, and Internal Resistance?

The relationship is given by $\epsilon = V + Ir$ or $V = \epsilon - Ir$. Here, $\epsilon$ is E.M.F., $V$ is terminal PD, $I$ is current, and $r$ is internal resistance.

What does the y-intercept of a $V$ vs $I$ graph represent?

The y-intercept represents the E.M.F. ($\epsilon$) of the source. This is because the y-intercept occurs where $I = 0$, and at zero current, the terminal potential difference equals the E.M.F.

Why does the terminal potential difference decrease as the external resistance decreases?

Decreasing external resistance increases the total current in the circuit. As $I$ increases, the 'lost volts' ($Ir$) across the internal resistance increase, leaving less potential difference ($V = \epsilon - Ir$) for the external circuit.

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Core Practical 3: Investigating E.M.F. & Internal Resistance

Summary

This practical investigation explores the relationship between the electromotive force (E.M.F.) of a power source and its internal resistance. By varying the external resistance in a circuit and measuring the resulting current and terminal potential difference, the internal resistance can be determined through graphical analysis of the linear relationship $V = \epsilon - Ir$ .

1. Definition & Core Concepts

Circuit diagram showing a cell with internal resistance r, an ammeter in series, a voltmeter in parallel to the cell, and a variable resistor R.

2. Underlying Principles

3. Methods & Techniques

Circuit Assembly: Connect a cell in series with an ammeter, a switch, and a variable resistor (rheostat). Connect a voltmeter in parallel across the terminals of the cell.
Data Collection: Close the switch and adjust the variable resistor to obtain a range of current ( $I$ ) and terminal voltage ( $V$ ) readings. It is essential to take at least 6-8 different readings to ensure a reliable line of best fit.
Minimizing Thermal Effects: Open the switch between readings. This prevents the cell from heating up, which would cause the internal resistance $r$ to change during the experiment, leading to non-linear data.
Range Selection: Choose a range of resistance that provides a significant change in current without exceeding the safety limits of the ammeter or causing excessive heating in the cell.

4. Key Distinctions

5. Exam Strategy & Tips

Graph of Terminal PD (V) against Current (I). The y-intercept is epsilon and the gradient is -r.

6. Common Pitfalls & Misconceptions