physical sciences experiment 2 internal resistance

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CTSC Gr. 12 PHYSICAL SCIENCES: Practical Experiment: Internal resistance in a battery

Build an electric circuit and use a known resistor to determine the internal resistance of the battery

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2024 GR 12 Experiment Internal Resistance

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Preview text, name of learner: ................................................................, school: ............................................................................., maximum mark 5 10 35 50, learner’s mark, vhembe east district, senior certificate, physical sciences, term 3 experiment – internal resistance, 19 july 2024, 1. background, the experiment to determine internal resistance is scheduled for the third term as, prescribed by caps. it falls in a section of electricity and magnetism. with all the, materials available, the experiment is fairly straightforward and easy to conduct., learners are expected to conduct the experiment as guided by the worksheets and, their teachers., to support learning and understanding, learners are advised to formulate answers to, questions in the last page as they conduct or after conducting the experiment. the, assessment composition, hints, report format, introduction, list of apparatus,, procedure and circuit diagram given below are meant to guide and to make it easy for, learners to work on the task., 2. assessment composition, learner assessment in this practical will occur in three parts or stages. part 1 or, stage 1 allows a teacher to assess the learners’ skills in conducting the, experiment. the second, part 2, is the evaluation of learners’ report about the, experiment. the two parts are credited 5 and 10 marks respectively. schools are, expected to, be done with part 1 and 2 assessment by end of business day on 19 th of july, part 3 of the task will be in form of a practical test. it will be administered out of, 35. the total will remain 50 marks. part 2 will be administered on the, 6. apparatus, voltmeter (or multi meter)., ammeter (or multi meter)., any size carbon zinc battery (choose voltage in relation to the values of the, resistors)., battery holder., connecting wires and a switch., (1) set up the apparatus as shown in the diagram overleaf., (2) set the rheostat to a particular position or setting, (3) close the switch and take both the voltage and current reading, (4) set the rheostat to a different position and take the reading as in 3 above, (5) take at least 5 sets of readings and record them appropriately, (6) use the readings as you build the report’, (7) use graph paper to draw a graph to analyse results, 7. precaution, do not keep the circuit on for too long – why, “it will heat the battery and cause it to run down”, as the experiment is conducted, readings of terminal voltage (volts) and electrical, current (amperes) must be recorded in table form. it is from this table that graphs and, all other interpretation must be based. (the teacher will elaborate further), 10. important instruction to learners, ▪ as you conduct the experiment, the teachers will assess you in your ways of, handling apparatus, ▪ you are expected to compile a report reflecting the elements mentioned under, report format., a short test will be administered on the 29 th of july 2024., 11. possible questions for the short practical test, a. identify the, i. independent variable., ii. dependent variable., iii. controlled variable., b. why do we include a rheostat in the circuit, c. draw a graph of the voltmeter readings versus ammeter readings, d. is the gradient of the graph positive or negative explain., e. use the graph to determine the internal resistance of the battery, f. which point on your graph represents the emf of the battery explain, g. draw a conclusion from the result, part two: experiment report assessment / marking tool - term 3, skill criteria mar k total, not given or not, related to the, tells what the, experiment intend to find, experiment or, incorrectly, well described., tells what the experiment, intends to find out., no variables, are identified, or one or all, variables are, incorrect [0], the independent,, dependent and control, variables are correctly, identified. [1] 1, apparatus are, mentioned or, just few are, all relevant apparatus are, procedure is, not given or is, given in a way, that does not, lead to the end, experiment [0], given but not, logically. it is not, procedure is logically and, completely described, experiment report assessment / marking tool (continue...) – term, skills criteria mark total, data is recorded, in tables but either, headings or units, are not indicated, data is well recorded in, suitable tables., columns have suitable, analysis or, interpretation, no analysis, attempted is, irrelevant. [0], results are well, analyzed. data is, represented, graphically. graphs are, accurately labeled., no conclusion, attempted /, conclusion has been, drawn and it connects, well with the variables., t o t a l 10, handling apparatus mark = / 5, experiment report mark = / 10, practical test mark = / 35, learner’s final experiment mark = / 50.

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A level physics online.

Practical - Internal Resistance

This experiment allows you to find physical constants from a graph.

Measuring Internal Resistance and EMF

1. Measuring Internal Resistance and EMF

You can calculate the internal resistance of a cell by changing the external resistance of the circuit and recording the terminal PD of the cell. When a graph is plotted the gradient is the negative value of 'r' while the y-intercept should be equal to the EMF of the cell.

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10.3 Batteries and internal resistance

10.3 batteries and internal resistance (escpv).

Up until now we have been dealing with ideal batteries in that they aren't affected by the circuit or current in any way and provide a precise voltage until they go flat.

If you measure the potential difference across the terminals of a battery on its own you will get a different value to what you measure when it is in a complete circuit. The value will be less when the battery is included in a complete circuit. Sometimes the difference is called the lost volts . Nothing has actually been lost but energy has been transferred.

Real batteries are made from materials which have resistance. This means that real batteries are not just sources of potential difference (voltage), but they also possess internal resistance. If the total potential difference source is referred to as the emf, \(\mathcal{E}\), then a real battery can be represented as an emf connected in series with a resistor \(r\). The internal resistance of the battery is represented by the symbol \(r\).

The external resistance in the circuit is referred to as the load.

Suppose that the battery with emf \(\mathcal{E}\) and internal resistance \(r\) supplies a current \(I\) through an external load resistor \(R\). Then the potential difference across the load resistor is that supplied by the battery:

Similarly, from Ohm's Law, the potential difference across the internal resistance is:

The potential difference \(V\) of the battery is related to its emf \(\mathcal{E}\) and internal resistance \(r\) by:

The battery is the source of energy and the energy provided per unit charge (emf) passing through the battery is equal to the total work done (potential difference) across the components in the circuit. This can be illustrated by showing the energy per unit charge as as function of the position in the circuit. The charge gains energy when moving through the battery and loses energy when moving through resistors.

• Postive work is done on a unit charge by the battery transferring an energy equal to the emf.
• The charge does work to overcome the internal resistance of the battery. Doing work requires that the charge lose some energy. The work done to overcome the internal resistance is \(V_{\text{internal resistance}}=Ir\).
• When the unit charge leaves the battery it has less energy than the original emf. This is now the total energy that it can use to do work moving through the circuit, \(V_{\text{load}} = \mathcal{E}-Ir\).
• As the charge moves around the circuit it does work passing through each component which is equal to \(IR\).

The emf of a battery is essentially constant because it only depends on the chemical reaction (that converts chemical energy into electrical energy) going on inside the battery. Therefore, we can see that the potential difference across the terminals of the battery is dependent on the current drawn by the load. The higher the current, the lower the potential difference across the terminals, because the emf is constant. For the same reason, the potential difference only equals the emf when the current is very small.

The current that can be drawn from a battery is limited by a critical, maximum value \({I}_{c}\). The more resistance in the circuit the less the current will be. Imagine that you have a wire with no resistance that you use to connect the terminals of the battery. The circuit is complete, current will flow and adding any resistance to the circuit would decrease the current. The current without any external resistance will be \({I}_{c}\). At a current of \({I}_{c}\), \(V=\text{0}\text{ V}\) because there is no load in the circuit. Then, the equation becomes:

The maximum current that can be drawn from a battery is less than \(\frac{\mathcal{E}}{r}\).

Worked example 6: Internal resistance

Determine the internal resistance of a battery that has an emf of \(\text{12,00}\) \(\text{V}\) and has a potential difference across its terminals of \(\text{10,00}\) \(\text{V}\) when a current of \(\text{4,00}\) \(\text{A}\) is flowing through the battery when connected in a circuit.

Determine how to approach the problem

It is an internal resistance problem. So we use the equation:

Solve the problem

Write the final answer.

The internal resistance of the battery is \(\text{0,50}\) \(\text{Ω}\).

Finding the internal resistance of a battery

To determine the internal resistance of a battery.

You will need the following items for this experiment:

battery / cell to be studied

electric leads

a set of resistors or a rheostat

We will set up a circuit that contains the battery we want to study in series with a resistor. Then we will measure the potential difference across the load as well as the current for a number of different resistors/rheostat in the circuit. It doesn't matter if it is a different resistor each time or more resistors in series or parallel. What matters is that the overall resistance of the circuit changes so that the current is different each time. The reason that doing this can tell us about the internal resistance of the battery is because the potential difference across the internal resistance is \(V_{\text{internal resistance}}=I\cdot r\) and we can vary I by changing the resistance of the circuit. If the potential difference across the internal resistance is changing and we add up all the potential differences, \(\mathcal{E} = V_{\text{load}}+V_{\text{internal resistance}}\) we can determine the internal resistance.

To do this we will actually plot a graph of \(V_{\text{load}}\) versus \(I\) and then use the features of the graph to determine \(\mathcal{E}\) and \(r\). To understand why plotting the graph will help us we start with the equation for the magnitude of the \(\mathcal{E}\) and substitute Ohm's Law and re-arrange as follows: \begin{align*} \mathcal{E} & = V_{\text{load}} + V_{\text{internal resistance}} \\ \mathcal{E} & = V_{\text{load}} + I\cdot r \\ V_{\text{load}}& = \mathcal{E} -I\cdot r \\ V_{\text{load}}& = -r\cdot I + \mathcal{E} \\ \underbrace{V_{\text{load}}}_{y}& = \underbrace{-r}_{m}\cdot\underbrace{I}_x + \underbrace{\mathcal{E}}_{c} \end{align*} If we plot \(V_{\text{load}}\) versus \(I\) we will be plotting data that are governed by this relationship. This allows us to conclude that the slope of the graph, \(m\), will be \(-r\) and the intercept vertical axis, \(c\), will be the emf \(\mathcal{E}\).

Record your results in a table like the one below. You can take more readings if you like.

Discussion and conclusion

Plot your data on a set of axes similar to this example. The blue crosses represent the measured data points, the gray, dashed line is the drawn straight line through the data points. The best fit line you draw doesn't need to go through all the data points, it should, in general, have as many points above and below the line. The slope of the line can be measured and equated to \(-r\) and the intercept with the vertical axis will give you \(\mathcal{E}\). The intercept with the horizontal axis would give you the maximum possible current the battery could deliver.

• Do your data form a perfectly straight line?
• What errors were introduced?