Q: How do you find EMF and internal resistance from a V-I graph? A: Plot terminal p.d. V against current I. In V=E−Ir, the y-intercept gives E, and the gradient is −r
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Chee Wei Jie·Academic Advisor (Physics)
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Fast graph answer For an internal resistance graph of terminal p.d. V against current I, use V=E−Ir. The y-intercept is the EMF E, and the gradient is −r. 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 r that limits current and wastes power. This guide shows how to measure r 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.
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.
Core Theory (The Exam Version)
For a battery with EMF E and internal resistance r:
V=E−Ir
Where:
V = Terminal voltage (what you measure)
I = Current through circuit
E = EMF (open-circuit voltage)
r = Internal resistance
Rearranging: V=−rI+E
This is a straight line with:
Gradient = −r
Y-intercept = E
Which Graph Gives EMF And Internal Resistance?
Use this table before drawing the graph:
Graph plotted
Straight-line form
What to read from the graph
Best use
V against I
V=−rI+E
Gradient =−r, y-intercept =E
Standard Paper 4 method
I against V
I=(E/r)−(1/r)V
Gradient =−1/r
V against load resistance R
Non-linear
Do not take a simple gradient for r
Qualitative trend only unless linearised
Power P against load resistance R
Non-linear peak
Maximum power occurs near R=r
Extension, not the fastest exam route
If the graph is V against I, keep the negative sign: a gradient of −2.4Ω means r=2.4ohm, not −2.4Ω.
Battery lab setup: what to connect first
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 V and I together, then plot V against I.
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. V against current I. 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 V=E−Ir.
internal resistance formula
Use V=E−Ir for a terminal-p.d. graph, or E=I(R+r) when the external load resistance is known.
how to find emf from vi graph
Extend the best-fit V-against-I line to I=0. The intercept on the voltage axis is the EMF.
internal resistance of a battery experiment
Vary the external resistance, record paired V and I readings quickly, then plot V against I.
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.
Keep current below the cell’s rated continuous current (check the datasheet)
Load resistance: 1-50 Ω
Expect r to increase steadily as the cell discharges
2. 9V Batteries
The surprise: Much higher internal resistance than AA cells.
Expect noticeably higher r even when fresh; it rises quickly with use
Current is limited; avoid very low resistances to prevent overheating
Why? Many 9V blocks house smaller cells in series, so resistance stacks.
3. Phone Power Banks
The complex beast:
Contains lithium cells plus protection and regulation circuits
Apparent r includes cable and converter losses
Use a USB tester/electronic load and observe the regulated output behaviour
Data Collection: Manual vs Automated
Manual Method (Exam-style)
Set resistance box to highest value
Record V and I
Decrease R in ~10 steps
Stop before I>1A (battery safety)
Plot immediately to check linearity
Pro tip: Take readings quickly - batteries heat up!
Arduino Automated Logger
// 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:
100+ data points in seconds
Captures transient effects
Export straight to Excel
Multiple batteries tested quickly
Temperature Effects (The Missing Chapter)
Why Temperature Matters
Internal resistance rises in the cold and falls modestly when warm (within safe limits).
Experimental Setup
Seal battery in zip-lock bag
Submerge in water bath
Wait 15 mins for thermal equilibrium
Measure r at each temperature
Plot r vs T
Safety: Don't heat above 50°C!
What You'll Find
Plotting r against temperature typically shows higher r at lower temperatures and lower r at moderate warmth; avoid temperatures outside the manufacturer’s safe operating range.
Advanced Analysis Techniques
1. Power Transfer Theorem
Maximum power delivered when Rload=r:
Pmax=4rE2
Experiment:
Vary R from 0.1r to 10r
Calculate P=I2R for each
Find peak power point
Verify Rpeak≈r
2. AC Impedance Method
Internal resistance has components:
DC resistance (ionic conduction)
AC impedance (capacitive effects)
Using function generator + oscilloscope:
Apply 1kHz sine wave
Measure voltage/current phase
Calculate complex impedance
3. Transient Response
Connect/disconnect load suddenly:
Voltage doesn't change instantly
Time constant τ=rC reveals battery capacitance
Relevant for pulse-discharge applications
Common Mistakes That Cost Marks
1. "My graph curves!"
Causes:
Battery heating during experiment
Approaching current limit
Protection circuit kicking in
Fix: Use lower currents, work quickly
2. "Negative internal resistance?"
You probably:
Swapped voltage/current axes
Connected ammeter in parallel
Have a regulated power bank
3. "Huge error bars"
Check:
Meter resolution (need 0.01V minimum)
Contact resistance (clean terminals!)
Wire resistance (use thick wires)
Data Analysis Template
Excel Setup
Parameters
A: Resistance (Ω)
B: Current (A)
C: Voltage (V)
D: =B*A Check:should≈C
Graph
Plot: C (y-axis) vs B (x-axis)
Trendline: Linear
Display: Equation + R²
Uncertainty Analysis
For each measurement:
δV=±0.01V (meter resolution)
δI=±0.01A (meter resolution)
δr=∣gradient∣×(VδV)2+(IδI)2
For gradient from graph:
Use LINEST function for uncertainty
Or calculate from worst-fit lines
Real-World Applications
Why This Matters Beyond Exams
Electric Vehicles
Battery pack r limits acceleration
Cold weather range reduction
Thermal management critical
Solar Systems
Battery bank sizing
Cable gauge selection
Inverter efficiency optimization
Portable Electronics
Fast-charging limits
Battery life estimation
Heat generation prediction
Exam-Style Questions You'll Ace
Q1: "Explain why terminal voltage drops under load"
Model answer: Internal resistance causes voltage drop Ir inside battery. Terminal voltage V=E−Ir decreases as current increases.
Q2: "Suggest improvements to reduce uncertainty"
Points to include:
Use lower currents (reduce heating)
Automate readings (minimize time)
Multiple batteries averaged
4-wire measurement for low r
Q3: "Why might r appear to change during experiment?"
Key factors:
Temperature rise from I2r heating
Chemical polarization at high currents
Battery capacity depletion
Protection circuit activation
Beyond the Basics: Research Extensions
1. Battery Chemistry Comparison
Alkaline vs NiMH vs Li-ion
How r changes with discharge state
Recovery effects after heavy load
2. Internal Resistance Spectroscopy
Measure r vs frequency (1Hz - 10kHz)
Reveals battery health/age
Used in battery management systems
3. Four-Wire (Kelvin) Measurement
Eliminates lead resistance
Essential for r<0.1 Ω
Industry-standard technique
Your Practical Exam Checklist
✓ Check meter zeros before starting ✓ Clean all contacts with alcohol ✓ Start with high R (low current) ✓ Work quickly to minimize heating ✓ Plot as you go to spot problems ✓ Multiple trials if time allows ✓ Calculate r 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.
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