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Q: How do you find EMF and internal resistance from a V-I graph?
A: Plot terminal p.d. against current . In , the y-intercept gives , and the gradient is
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Fast graph answer
For an internal resistance graph of terminal p.d. against current , use . The y-intercept is the EMF , and the gradient is . A steeper negative gradient means a larger internal resistance.
TL;DR
That "ideal battery" in your circuit diagram? It doesn't exist. Every real battery has internal resistance that limits current and wastes power. This guide shows how to measure for different battery types, automate data collection with Arduino, and understand why your phone charger gets warm. Essential for scoring in H2 Physics Paper 4's favourite circuit practical.
Working through the other Paper 4 staples too? Pair this experiment with our H2 Physics Practical 2026 guide, then keep it in rotation via the H2 Physics practicals hub so your logbook covers every waveform, fields, and thermal investigation SEAB loves to test.
Status: SEAB's 2026 H2 Physics 9478 syllabus places internal resistance under Current of Electricity and Circuit Systems, and Paper 4 assesses practical skills. Use this page as a graph-method guide, not a claim that this exact battery setup will appear in a given examination year.
Looking for structured Paper 4 coaching? See our H2 Physics tuition programme.
Your textbook shows:
What actually happens: internal resistance rises as cells discharge, increases further in the cold, and varies by chemistry and construction. This explains why torches dim as batteries flatten and why fast-charging slows when a phone is cold.
For a battery with EMF and internal resistance :
Where:
Rearranging:
This is a straight line with:
Use this table before drawing the graph:
| Graph plotted | Straight-line form | What to read from the graph | Best use |
| against | Gradient , y-intercept | Standard Paper 4 method | |
| against | Gradient | ||
| against load resistance | Non-linear | Do not take a simple gradient for | Qualitative trend only unless linearised |
| Power against load resistance | Non-linear peak | Maximum power occurs near | Extension, not the fastest exam route |
If the graph is against , keep the negative sign: a gradient of means , not .
For a school-lab internal resistance experiment, build the circuit before taking any readings:
| Step | Check |
| 1 | Put the ammeter in series with the cell and load. |
| 2 | Put the voltmeter across the cell terminals, not across the external resistor. |
| 3 | Start with the largest load resistance so the current is small. |
| 4 | Close the switch only while taking each reading, then open it again. |
| 5 | Record and together, then plot against . |
This setup directly answers the common graph question: the y-intercept estimates the EMF, while the magnitude of the gradient estimates the internal resistance.
| Search phrase | First answer |
| internal resistance graph | Plot terminal p.d. against current . The y-intercept is EMF and the magnitude of the negative gradient is internal resistance. |
| internal resistance experiment graph | Use 6 to 10 load settings, open the switch between readings, then draw one best-fit straight line before calculating the gradient. |
| emf and internal resistance graph | Read EMF from the y-intercept and internal resistance from the magnitude of the negative gradient in . |
| internal resistance formula | Use for a terminal-p.d. graph, or when the external load resistance is known. |
| how to find emf from vi graph | Extend the best-fit -against- line to . The intercept on the voltage axis is the EMF. |
| internal resistance of a battery experiment | Vary the external resistance, record paired and readings quickly, then plot against . |
| battery in physics lab | Use a small cell or battery pack within safe current limits, start with the largest resistance, and stop if the cell warms noticeably. |
| battery internal resistance diagram | Put the ammeter in series and the voltmeter across the cell terminals. If the voltmeter is across the external resistor instead, the graph no longer measures the cell's terminal p.d. directly. |
For the full Paper 4 route, keep this graph answer beside the H2 Physics Practical 2026 guide and the H2 Physics Paper 4 technique file.
[Battery] --+-- [Ammeter] --+-- [Variable Resistor]
| |
+--[Voltmeter]--+Variable Resistor Options:
Measurement Tools:
Setup specifics:
The surprise: Much higher internal resistance than AA cells.
Why? Many 9V blocks house smaller cells in series, so resistance stacks.
The complex beast:
Pro tip: Take readings quickly - batteries heat up!
// Simplified code structure
// Uses INA219 current/voltage sensor
#include <INA219.h>
void loop() {
float voltage = ina.getBusVoltage();
float current = ina.getCurrent();
Serial.print(voltage);
Serial.print(",");
Serial.println(current);
delay(100); // 10 readings per second
}Advantages:
Internal resistance rises in the cold and falls modestly when warm (within safe limits).
Safety: Don't heat above 50°C!
Plotting against temperature typically shows higher at lower temperatures and lower at moderate warmth; avoid temperatures outside the manufacturer’s safe operating range.
Maximum power delivered when :
Experiment:
Internal resistance has components:
Using function generator + oscilloscope:
Connect/disconnect load suddenly:
Causes:
Fix: Use lower currents, work quickly
You probably:
Check:
Parameters
Graph
For each measurement:
For gradient from graph:
Model answer: Internal resistance causes voltage drop inside battery. Terminal voltage decreases as current increases.
Points to include:
Key factors:
✓ Check meter zeros before starting
✓ Clean all contacts with alcohol
✓ Start with high (low current)
✓ Work quickly to minimize heating
✓ Plot as you go to spot problems
✓ Multiple trials if time allows
✓ Calculate from gradient, not individual points
✓ Discuss temperature in evaluation
Master this practical and you'll not only secure full marks - you'll understand why your phone battery meter lies, why jump-starting works, and why battery technology remains the bottleneck in our electric future.
View our sample completion document (Current sample layout (design may be refined over time))
| Less direct, but still valid if the question gives this graph |