Physics · Year 12 · Charge and Current · Autumn Term

Electromotive Force (EMF) and Internal Resistance

Students will define EMF and internal resistance, analyzing their effects on terminal potential difference in circuits.

• National Curriculum Attainment Targets
• A-Level: Physics - Electricity
• A-Level: Physics - DC Circuits

About This Topic

Electromotive force (EMF) represents the maximum potential difference a cell or power source can provide when no current flows. Students learn that real batteries include internal resistance, which reduces the terminal potential difference to V = E - Ir when current I passes through. This equation shows how voltage drops under load, limiting power delivery in circuits.

This topic fits within A-Level Physics Electricity, specifically DC circuits in the Charge and Current unit. Students address key questions: they explain internal resistance's impact on power output, analyze factors causing voltage drops, and design experiments to measure a battery's internal resistance. These concepts prepare students for advanced topics like circuit efficiency and power transfer theorems.

Active learning benefits this topic greatly because students build and test real circuits. When they measure voltages across variable loads, plot V-I graphs in small groups, and compare results, abstract relationships become visible through their data. This hands-on process builds confidence in experimental design and data analysis, key A-Level skills.

Key Questions

1. Explain how internal resistance affects the power delivered by a real battery.
2. Analyze the factors that cause a battery's terminal voltage to drop under load.
3. Design an experiment to determine the internal resistance of a power source.

Learning Objectives

• Calculate the terminal potential difference of a cell given its EMF, internal resistance, and the current flowing.
• Analyze the relationship between internal resistance, load resistance, and power dissipated by the external circuit.
• Design and describe an experimental procedure to determine the EMF and internal resistance of a given power source.
• Explain how internal resistance causes a real battery's voltage to decrease as current increases.
• Compare the efficiency of power transfer from a real cell to different external resistances.

Before You Start

Ohm's Law and Simple Circuits

Why: Students need a solid understanding of Ohm's Law (V=IR) and how to analyze basic series and parallel circuits before introducing the complexities of internal resistance.

Electric Potential Difference and Current

Why: A foundational grasp of what electric potential difference (voltage) and electric current represent is essential for comprehending EMF and voltage drops.

Key Vocabulary

Electromotive Force (EMF)	The total energy converted from chemical to electrical energy per unit charge passing through a source, measured in volts. It represents the ideal voltage of a power source when no current is drawn.
Internal Resistance (r)	The resistance within a power source, such as a battery, due to the materials it is made from. This resistance causes a voltage drop within the source itself when current flows.
Terminal Potential Difference (V)	The actual potential difference measured across the terminals of a power source when current is flowing. It is less than the EMF due to the voltage drop across the internal resistance.
Voltage Drop	The reduction in electrical potential along the path of a current, especially across a resistance. In a real cell, this occurs across the internal resistance.

Watch Out for These Misconceptions

Common Misconception

EMF equals terminal potential difference at all times.

What to Teach Instead

Terminal PD drops below EMF due to Ir drop across internal resistance when current flows. Active circuit-building lets students measure this drop directly, contrasting open-circuit readings with loaded ones to revise their models through evidence.

Common Misconception

Internal resistance only affects weak batteries.

What to Teach Instead

All real power sources have internal resistance; its effect scales with current. Group experiments with fresh and used batteries reveal consistent patterns, helping students generalize via shared data discussions.

Common Misconception

Power output increases indefinitely with load current.

What to Teach Instead

Power peaks at specific current due to internal resistance trade-off. Plotting activities show the parabolic curve, where students derive the condition I = E/(2r) collaboratively.

Active Learning Ideas

Pairs Experiment: Internal Resistance Measurement

Pairs connect a battery, high-resistance voltmeter, and variable load resistor in series. They record terminal PD for currents from 0 to 0.5 A using an ammeter. Students plot V against I; the gradient gives -r and y-intercept gives EMF. Discuss sources of error.

45 min·Pairs

Small Groups: Power Delivery Circuits

Groups assemble circuits with a battery and three load resistors. They measure current, terminal PD, and calculate power for each load. Compare power outputs to identify maximum power point. Groups present findings on how internal resistance limits efficiency.

50 min·Small Groups

Whole Class Demo: Open vs Load Voltage

Demonstrate open-circuit voltage with voltmeter only, then add loads to show drop. Class predicts and records values on shared whiteboard. Follow with paired predictions for a new battery using prior data.

30 min·Whole Class

Individual Graph Analysis: V-I Plots

Provide printed V-I data sets from different batteries. Students graph manually, determine E and r, then compare ideal vs real sources. Extend to calculate maximum power.

25 min·Individual

Real-World Connections

• Electrical engineers designing portable electronic devices, like smartphones and laptops, must account for battery internal resistance to ensure consistent performance and predict battery life under varying usage loads.
• Automotive technicians diagnose starting problems in vehicles by measuring battery voltage under load, identifying weak batteries where high internal resistance prevents sufficient current flow to the starter motor.
• Researchers developing advanced battery technologies for electric vehicles focus on minimizing internal resistance to maximize power output for acceleration and improve overall energy efficiency.

Assessment Ideas

Quick Check

Present students with a circuit diagram showing a battery with EMF E and internal resistance r, connected to an external resistor R. Ask them to write down the equation for the terminal potential difference and the current flowing in the circuit. Then, ask them to calculate the terminal voltage if E = 6.0 V, r = 0.5 Ω, and R = 5.0 Ω.

Discussion Prompt

Pose the question: 'Imagine you have two identical batteries, but one has a significantly higher internal resistance. How would this difference affect the power delivered to a small motor connected to each battery, and why?' Facilitate a class discussion focusing on the concepts of voltage drop and power efficiency.

Exit Ticket

Provide students with a graph plotting terminal voltage against current for a real cell. Ask them to identify the EMF and the internal resistance from the graph. Then, ask them to predict the terminal voltage if the current were doubled.

Frequently Asked Questions

What is electromotive force and internal resistance?

EMF is the open-circuit potential difference of a power source, representing work done per unit charge by chemical reactions. Internal resistance is opposition to current flow within the source itself, causing terminal PD to be V = E - Ir. Students model this in circuits to see real-world limitations on voltage and power.

How does internal resistance affect power delivered by a battery?

Internal resistance causes voltage drop proportional to current, so power P = I(V) = I(E - Ir) peaks at I = E/(2r). Beyond this, losses dominate. Experiments with variable loads quantify this, matching theory to data for deeper insight.

How can active learning help teach EMF and internal resistance?

Active approaches like paired circuit construction and graphing V vs I make equations tangible. Students collect their own data, spot trends in real time, and troubleshoot errors collaboratively. This builds experimental skills and counters passivity, as predictions tested against measurements reinforce understanding of voltage drops.

How to design an experiment to find a battery's internal resistance?

Use a battery, variable resistor (potentiometer), ammeter, and voltmeter in series. Vary load to change I from near zero to half max, measure V each time. Plot V vs I: straight line with gradient -r, intercept E. Repeat for reliability; control temperature.