circuitsInvestigation

Electrical Circuits: Investigation of Internal Resistance of Batteries

Year 11 Physics - Thomas Han 2023

EMF, Internal resistance, Terminal Potential Difference and Lost Volts

Devices supplying electrical energy are called electric sources. The main power source in our experiment is a power supply, specifically a battery.

The electromotive force (EMF), E, of a source is the energy supplied to each coulomb of charge which passes through the source. It is commonly measured in volts, V. (Physics, Mr Mitchell, 2023)

Consider the circuit below which has a battery, a voltmeter, load resistor, R, and switch, S.

(Fig 1: a basic circuit featuring a battery, a voltmeter, load resistor and as which made from tools at circuit-diagram.org)

When the switch is open, the circuit is called an open circuit, where no current is flowing. In this scenario, the voltmeter gives the EMF. If the battery was 6V, the voltmeter in an open circuit would show 6V.

However, when the switch is closed, current is able to flow through the circuit. In the real world, as all materials have some sort of resistance, the power supply must have its own resistance, called the internal resistance, r. This means we can model a power supply of electrical energy (battery) in series with a small resistance (internal resistance), as show in Fig 2.

(Fig 2: Real Source)

In a closed circuit with a battery with an internal resistance, if we attempt to measure the volts, the measured volts will usually be lower than volts output by the battery. The voltmeter connected to the variable supply measures the potential difference, Vtpd.

If we link our power supply without a circuit, (the switch is turned off), there is no current to the battery, and we can get our maximum voltage. (The Physics Classroom, 2022)

·       When current is drawn from an electrical source, some energy is wasted inside the source due to its internal resistance. This is referred to as the lost vaults, Vlost.

·       This means that there is less voltage available to the load resistor, R. The voltage available at the terminals of the electrical source, and therefore across the load resistor, is called the terminal potential difference (tpd), Vtpd.

·       By conservation of energy,

or

where:

-       E is the electromotive force measured in Volts (V). -       V is terminal potential difference measured in Volts (V). -       I is current measured in Amperes (A). -       R is internal resistance measured in ohms (Ω). The equation can be rewritten as and factorised into .

Questions Q. If a source (battery) had zero internal resistance what would happen if the battery was shorted out?

If a battery with zero internal resistance is shorted out (connected directly with a wire across its terminals), theoretically, an infinite amount of current would flow through the circuit. This is because the internal resistance of the battery is responsible for limiting the current that flows through it. With zero internal resistance, there would be no resistance to the flow of electrons, resulting in an extremely high current.

Q. If we measure the voltage of the source when current flow is zero, what is the PD across this resistance and how would voltage measured compare to the emf? If you measure the voltage of the source when there is zero current flowing through it (open circuit conditions), you would be measuring the electromotive force (emf) of the source. This is because the entire voltage drop would occur across the source itself, and none across any internal resistance. So, the voltage measured in this scenario would be equal to the EMF of the source.

Q. Voltmeters have a high resistance but not infinite, is it possible to get a 100% accurate reading of emf using a voltmeter? While voltmeters have high resistance, they are not truly infinite in resistance. In practical terms, they have very high resistance compared to the components they are connected to, and this minimizes the current drawn from the circuit being measured. This is done to ensure that the voltmeter doesn’t significantly affect the circuit it’s measuring.

However, due to the finite resistance of the voltmeter, it will draw a small amount of current from the circuit it’s measuring, and this can cause a slight voltage drop across the internal resistance of the source. This means that when you measure the voltage across the terminals of the source using a voltmeter, you might measure a value slightly lower than the actual emf of the source.

Post-Lab Discussion

1.     Use a graphical method to obtain emf and r from either slopes or intercepts of your raw or manipulated data. How do these values compare with the values you obtained by direct measurement?

The internal resistance, r, is the absolute value of the slope of the graph.

Green r is 1.7 ohms, Yellow r is 1.6 ohms, Red r is 2.9 ohms.

The emf can be found by the y intercepts of our data. Using the graph, we draw a line of best fit and measure the y intercepts, we find that:

Green emf is 5.6 volts, Yellow emf is 5.5 ohms, Red emf is 5.3 ohms.

2.     How do the emf and internal resistance of a flat dry cell compare with those of a fresh dry cell?

Over time the conductivity of the cell contents decreases, thus increasing the internal resistance of the cell. The instantaneous EMF drops too; but the standard cell EMF does not as the standard EMF depends on electrolyte used. (Kundu, 2017)

3.     How does the internal resistance of an alkaline battery compare with that of a heavy-duty battery of the same size and shape?

Generally, alkaline batteries have lower internal resistance compared to heavy-duty batteries of the same size and shape. Alkaline batteries can deliver energy more efficiently, and heavy-duty batteries, on the other hand, tend to have higher internal resistance, making them less suitable for applications that require higher currents or consistent power output. (Machine Design, 2022)

4.     The battery in a torch has been used for a long time. Explain why the torch is dim even though the emf of each cello is the same as when they were first bought.

As a battery in a torch is used over time, its internal resistance increases, causing voltage drops and reduced energy delivery. The battery stores a finite amount of chemicals, which deplete as energy is being used. When the chemicals become low in quantity, reactions will become negligible, and electricity available also becomes negligible. This is the discharging process of battery, causing the light to be dimmer. (Deshpande, 2018)

5.     Does a power pack have internal resistance? Explain your answer.

Yes. All power supplies have some resistance between their terminals called internal resistance. This causes charges in the circuit to dissipate some electrical energy in the power supply itself. The power supply becomes warm when delivering a current. (O’Hanlon, n.d.) Materials used in power sources are not perfect conductors. Microscopic impurities, crystal defects, and other imperfections within materials can create localized areas of higher resistance.

Bibliography §

Deshpande, R. (2018). When a battery in a torch is used for several weeks, the light from its bulb becomes dim. We say that the battery or cell is discharged. What does it mean? Retrieved from Quora: https://www.quora.com/When-a-battery-in-a-torch-is-used-for-several-weeks-the-light-from-its-bulb-becomes-dim-We-say-that-the-battery-or-cell-is-discharged-What-does-it-mean#:~:text=And%20after%20using%20the%20battery,bulb%20become%20dull%20for%20that.

Kundu, A. (2017). How does EMF and internal resistance of a dry cell change with time? Retrieved from Quora: the conductivity of the cell contents, thus increasing the internal resistance of the cell. The instantaneous EMF drops too; but the standard cell EMF does not; as the standard EMF depends on electrolyte used.

Machine Design. (2022, November 15). Batteries. Retrieved from Machine Design: https://www.machinedesign.com/automation-iiot/batteries-power-supplies/article/21832782/batteries

O’Hanlon, T. (n.d.). INTERNAL RESISTANCE. Retrieved from PATHWAYZ: https://www.pathwayz.org/Tree/Plain/INTERNAL+RESISTANCE

Physics, Mr Mitchell. (2023, 1 12). Higher Physics | Electricity | EMF & Internal Resistance | THEORY. Retrieved from YouTube: https://youtu.be/oUp4KKx2COU?si=I-6zPvPhe7SBTWpC

The Physics Classroom. (2022). Electric Circuits - Lesson 4 - Circuit Connections. Retrieved from The Physics Classroom: https://www.physicsclassroom.com/class/circuits/Lesson-4/Series-Circuits

Data

GREEN LABELED BATTERIES			YELLOW LABELED BATTERIES			RED LABELLED BATTERIES
current	voltage	variable resistance	current	voltage	variable resistance	current	voltage	variable resistance
0.48	4.74	10	0.47	4.72	10	0.4	4.12	10
0.25	5.11	20	0.25	5.02	20	0.22	4.62	20
0.11	5.35	50	0.11	5.26	50	0.1	4.96	50
0.05	5.45	100	0.06	5.34	100	0.05	5.12	100
0.03	5.5	200	0.03	5.4	200	0.03	5.21	200
0.01	5.55	500	0.01	5.43	500	0.01	5.27	500