Q: What does Internal Resistance of Batteries: Beyond the Textbook for H2 Physics cover? A: Move beyond dry cells to test AA batteries, 9V blocks, and phone power banks.
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.
The Reality Check Your Textbook Skips
Your textbook shows: E=I(R+r)
What actually happens:
Fresh AA battery: r≈0.1 Ω
After 50% discharge: r≈0.3 Ω
Cold battery at 0°C: r doubles
Old 9V battery: r>10 Ω
This isn't just exam fodder - it's why your torch dims as batteries die, and why electric cars struggle in winter.
Core Theory (The Exam Version)
For a battery with EMF E and internal resistance r:
Why? Six tiny 1.5V cells in series = 6x the resistance
3. Phone Power Banks
The complex beast:
Contains lithium cells + protection circuits
Apparent r includes electronics
Output may be regulated (constant V)
Need USB tester for proper measurements
Typical results:
Good 10,000mAh bank: rapparent≈0.2 Ω
Includes cable resistance!
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 changes dramatically:
Room temp (25°C): Baseline r
Fridge (4°C): r increases ~50%
Freezer (-18°C): r doubles or more
Hot car (45°C): r decreases ~20%
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
For alkaline batteries:
r(T)≈r25°C×e−b(T−25)
Where b≈0.02 K⁻¹
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.
Internal Resistance of Batteries: Beyond the Textbook for H2 Physics
