What is the difference between e.m.f. and terminal potential difference in a practical circuit?

E.m.f. is the total energy supplied per unit charge by the source, while terminal p.d. is the energy per unit charge available to the external circuit. They differ by the 'lost volts' ($Ir$) dissipated across the internal resistance.

How does the terminal voltage change as the external load resistance decreases?

As load resistance decreases, the total circuit current increases. This leads to a higher value of 'lost volts' ($Ir$), which causes the terminal potential difference ($V = \epsilon - Ir$) to decrease.

Why is a high-resistance voltmeter used to measure e.m.f. in an open circuit?

A high-resistance voltmeter draws negligible current from the cell. Since $V = \epsilon - Ir$, if $I$ is approximately zero, the terminal p.d. measured by the voltmeter is effectively equal to the e.m.f.

What is the most common systematic error in the E.M.F. and Internal Resistance practical?

The most common systematic error is the heating of the cell. If the switch is left closed, the internal resistance may increase due to temperature changes, causing the $V-I$ relationship to become non-linear.

What error occurs if current is plotted in mA without conversion on a $V-I$ graph?

The gradient of the graph will be off by a factor of 1000. Since $r = -gradient$, the calculated internal resistance would be 1000 times smaller than the true value in ohms.

Why should you avoid using run-down batteries for this experiment?

Run-down batteries often have an e.m.f. and internal resistance that fluctuate significantly during the experiment. This introduces random errors and makes it difficult to obtain a consistent straight-line graph.

Define 'lost volts' in the context of a power supply.

Lost volts is the potential difference dropped across the internal resistance of a cell when current flows. It is calculated as the product of the current and the internal resistance ($v = Ir$).

State the equation relating e.m.f., terminal p.d., and internal resistance in the form of a straight line.

The equation is $V = -rI + \epsilon$. In this form, $V$ is the y-variable, $I$ is the x-variable, $-r$ is the gradient, and $\epsilon$ is the y-intercept.

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

The x-intercept represents the 'short-circuit current'. This is the maximum possible current the cell can deliver when the external resistance is zero, calculated as $I_{max} = \frac{\epsilon}{r}$.

Why is a variable resistor used instead of several fixed resistors?

A variable resistor allows for continuous and rapid adjustment of the circuit current. This makes it easier to collect a large number of data points across a specific range to improve the accuracy of the line of best fit.

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Core Practical 8: Investigating E.M.F. & Internal Resistance

Summary

This practical investigation explores the relationship between the electromotive force (e.m.f.) and internal resistance of a power source. By varying the external load resistance and measuring the resulting terminal potential difference and current, students can graphically determine the e.m.f. and internal resistance using the linear relationship $V = -rI + \epsilon$ .

1. Definition & Core Concepts

Electromotive Force (e.m.f., $\epsilon$ ): This represents the total energy transferred by a power supply per unit charge. It is measured in volts (V) and is equivalent to the potential difference across the terminals of the supply when no current is flowing (open circuit).
Internal Resistance ( $r$ ): Every real power supply has an inherent resistance to the flow of charge within itself. This causes some electrical energy to be dissipated as heat inside the battery, leading to a drop in the voltage available to the rest of the circuit.
Terminal Potential Difference ( $V$ ): This is the actual voltage delivered to the external circuit (the load). It is always less than the e.m.f. when a current is flowing due to the 'lost volts' across the internal resistance.
Lost Volts ( $v$ ): The potential difference dropped across the internal resistance, calculated as $v = Ir$ . It represents the energy per unit charge wasted as heat within the power source.

2. Underlying Principles

A graph of Terminal Potential Difference (V) against Current (I) showing a negative linear relationship where the y-intercept is the e.m.f. and the gradient is the negative internal resistance.

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips