Physics Higher Level
Internal Assessment
Investigating the internal resistance of a battery
“How does the external resistance of a circuit affects the voltage drop across a 3V battery?”
Personal code: ggp356
Word count: 1998
Introduction
I have chosen this topic as my IB Physics HL investigation as I have always been fascinated with electricity since I was young especially with batteries. I tend to do an experiment on batteries with my brother such as connecting it to a small DC motor which makes the DC motor to work, connecting it to a small lamp which makes the lamp glow, connecting it to an aluminum foil which makes up the heat and used it as a fire start up. All of these experiments done by me and my brother back in the days was driven by our curiosity on what could a battery do rather than only acting as a power supply to small electrical appliances such as baby toys and television remote control. I remember I made my first simple circuit using a battery and a DC motor which I used for my handmade boat and turns out it worked! With a battery, we could make any of small electrical appliances from a clock to as simple as a calculator to work.
During my IB Physics class, I learned more about batteries such as what happened inside a battery when you connect it to a lamp for example, I learned how the electrons moved inside the battery and also how the resistance inside the battery (internal resistance) and resistance in a circuit affects the difference in the voltage drop. This drives my curiosity on batteries which motivate me to do this investigation and finding the answer of:
“How does the external resistance of a circuit affects the voltage drop across a 3V battery?”
EXPLORATION
First of all, what is a battery? “Battery or an electric cell is a device that uses the energy stored in chemicals to arrange charges in such way that a potential difference is created which can be used to cause a current flow in a conductor. The internal components of a cell have resistance, so when current flows from the cell some energy is lost.”
Figure 1 – Diagram of a battery
This resistance is represented in above diagram as r usually in circuit diagram is placed next to the symbol for a cell. Apart from internal resistance, there is the Emf () or electromotive force which is the work done per unit charge that takes the charge from the low potential to the high potential. This energy has been transferred from the chemical energy so the emf of the cell is the amount of chemical energy transferred to electrical potential energy per unit charge. The unit of emf is volt (V).
If there’s no current flows through the cell, there will be no voltage drop across the internal resistance. The potential difference across the terminals of the battery would be equal to the emf. However, if current flows the terminal potential difference would be less than the emf because the internal resistance of the cell resists the flow of current. In order to find internal resistance we must apply Ohm’s law to the internal resistance which made the potential difference will be Ir giving the formula:
Rearranging this formula, we can get an equation for the internal resistance from the battery:
According to the formula above, R is the external resistance which lies outside the battery but within the circuit. This external resistance is inversely proportional to the current within the circuit which means when there is an increase in the external resistance, the current of the circuit decreases and vice versa. However, this external resistance is directly proportional to the terminal voltage which means an increase in external resistance also increases in the terminal voltage.
The purpose of this investigation is to explore the relation between external resistance and the voltage drop, how does the external resistance affect the voltage drop. This voltage drop is obtained by subtracting the terminal voltage with the Emf ( of the 3V battery and the external resistance is provided by a resistance box. My hypothesis towards this investigation is that the external resistance will affect the voltage drop across the 3V battery, the voltage drop will decrease as the external resistance increases.
Manipulation of variables
• Independent variable
– The independent variable will be the external resistance and I am using a resistance box varying from 0 until 10. The reason I took the resistance box is that the value of the data would large enough to calculate instead of using the resistance box which makes the value of the data smaller and hard to calculate and also to reduce random error. Since resistance box is an analog device, the uncertainty of this device is 0.1. In this investigation, I took the range from 0 till 10 in order to support my result.
• Dependent variables
– The first dependent variable would be the voltage drop and to be obtained by subtracting the terminal voltage with the emf of the battery. To measure the terminal voltage, I used a multimeter rather than using the normal voltmeter in order to increase the accuracy of the data shown. In order to reduce random error, I have taken 3 trials of the terminal voltage. Since it is a digital device, the uncertainty of the multimeter is 0.01V.
– The second dependent variable would be the current. The current in the circuit would determine the internal resistance of the battery by plotting voltage drop vs current graph and the slope of the graph provide us with the internal resistance. I took the current for one trial only because in this investigation I am more focused on the terminal voltage and the external resistance. The current is measured using a multimeter in order to increase the accuracy of the data and since multimeter is a digital device, the uncertainty of the multimeter is 0.01V.
• Controlled variables
– The controlled variable is the number of cells that I used in this investigation. I have used two 1.5V cells which added up to 3V batteries. I used 3V battery in order to make the value of the data easy to calculate. If I used only one 1.5V cell the data would be too small and hard to calculate.
Figure 2 – Circuit Diagram
Apparatus:
– Two multimeter for measuring volt (0.01V) and current (0.01A)
– Two 1.5V cell ()
– One resistance box () (0.1)
– A switch
Figure 3 – The Apparatus
Safety precautions
In this investigation, I will be dealing with electricity which can be dangerous if we do not treat it with care. In this experiment I am using the tools and equipment with non-conducting handles only to prevent electrical shock. Other precautions also needs to be considered like avoid contacting circuits with wet hands, do not keep highly flammable substances near electrical equipment, keep access to electrical panels and open the switch when the experiment are done.
Methods:
1. Set up the apparatus as in figure 2 and connect all apparatus. Use one of the multimeter to measure the terminal voltage of the 3V battery (parallel) and the other multimeter for measuring the current throughout the circuit (series). Keep the resistance box at 0 and keep the switch open so that no current is flowing through the current which can drain the charge inside the battery.
2. Closed the circuit. Both of the multimeter will began to show some values and record this values of the terminal voltage and current in separate sheet of paper. After recording these values, began in increasing the external resistance by turning the resistance box to 1 and then record the terminal voltage and its current.
3. Repeat step 2 by keep increasing the external resistance one-by-one until 10.
4. These values are only trial 1 and in order to gain values for trial 2 and trail 3, repeat step 2 and 3.
5. After doing all of the three trials, open the switch to stop the current from flowing.
6.
ANALYSIS
External resistance (0.1)
()
Current (0.01A)
Emf (
Terminal Voltage (0.01V)
Trial 1
Trial 2
Trial 3
0.0
0.48
3.0
1.32
1.12
1.14
1.0
0.41
3.0
1.54
1.32
1.28
2.0
0.35
3.0
1.71
1.44
1.44
3.0
0.31
3.0
1.85
1.59
1.58
4.0
0.28
3.0
1.94
1.69
1.67
5.0
0.25
3.0
2.02
1.78
1.75
6.0
0.23
3.0
2.09
1.86
1.84
7.0
0.21
3.0
2.15
1.92
1.90
8.0
0.19
3.0
2.19
1.96
1.96
9.0
0.18
3.0
2.24
2.03
2.01
10.0
0.16
3.0
2.29
2.10
2.07
Table 1 – Raw Data Table
• Since I am using a resistance box to supply the resistance to the circuit, the uncertainty of the device is the least count which is 0.1.
• The current is measured using a multimeter which is a digital device and its uncertainty are the least count and that is 0.01A.
• The Emf ( is added up which becomes 3V and the emf remains constant throughout the experiment.
• The terminal voltage is measured using a multimeter which is a digital device and its uncertainty are the least count and that is 0.01V.
•
External resistance (0.1)
(
Current (0.01A)
Emf (
Average Terminal Voltage (0.1V)
Voltage drop (0.1V)
0.0
0.48
3.0
1.19
1.81
1.0
0.41
3.0
1.38
1.62
2.0
0.35
3.0
1.53
1.47
3.0
0.31
3.0
1.67
1.33
4.0
0.28
3.0
1.77
1.23
5.0
0.25
3.0
1.85
1.15
6.0
0.23
3.0
1.93
1.07
7.0
0.21
3.0
1.99
1.01
8.0
0.19
3.0
2.04
0.96
9.0
0.18
3.0
2.09
0.91
10.0
0.16
3.0
2.15
0.85
Table 2 – Processed Data Table
• The average terminal voltage is gained by adding all of the three trials of each resistance and then divide it by 3.
• The uncertainty of the average terminal voltage is found by calculating the difference between the maximum and minimum values of the terminal voltage and dividing by 2: which is 0.1V.
• The voltage drop is found by subtracting the emf with the average terminal voltage: () and the uncertainty remains the same with the average terminal voltage which is 0.1V.
Graph 1 – Voltage Drop vs Current graph
• From the graph above, the slope of the graph provides us with the internal resistance of the battery and its gradient is 3.035 0.05, the maximum slope is 3.623 and the minimum slope is 2.386.
• The uncertainty of the slope can be found using this formula which shows and the result is 0.6275.
• I used the same formula to find the y-intercept which is subtituting and the result is ±0.1970.
From the processed data, we can see that the voltage drop decreases as the external resistance increases. Same goes to the the current of the circuit, this is because current is always inversely proportional to the resistance. However, the terminal voltage increases as the external resistance increases, this is because terminal voltage is directly proportional to the external resistance according to Ohm’s Law. This processed data supports my hypothesis on the effect of external resistance towards the voltage drop.
Conclusion
Recalling my research question of this investigation: “How does the external resistance of a circuit affects the voltage drop across a 3V battery?”, from the raw data I took three trials of the terminal voltage in order to make my data more accurate and also reducing the random error. The processed data shows that the voltage drop decreases as the external resistance increases that same goes to the the current of the circuit. This is because Ohm’s Law where current is always inversely proportional to the resistance. In the other hand, the terminal voltage increases as the external resistance increases, this is because terminal voltage is directly proportional to the external resistance according to Ohm’s Law. This shows that the greater the external resistance is, the less voltage drop there will be and cause more less energy loss because of greater resistance. From the voltage drop vs current graph, all of the points are in straight line which means it strongly support my hypothesis. The slope of the graph provide us with the internal resistance which has been calculated using: , the reason I took the current as my dependent variable is because I need it for calculating the internal resistance. And from this it shows that as the external resistance increases, automatically the internal resistance inside the battery increases. The data supports my hypothesis on the effect of external resistance towards the voltage drop, therefore, external resistance does have affect the voltage drop across 3V battery.
In this investigation, there are several occasions that can cause an error although I already reducing it by taking three trials. Firstly, the reading on the multimeter sometimes changing by its own although I didn’t touch the apparatus. To reduce this random error, taking more than three trials is required in order to get the average value and increase its accuracy of the data. Secondly when recording the data, the circuit is closed which drains the charges from the battery which can affect the next recorded value. To overcome this random error, when writing the readings, the switch must be opened in order to keep the charges in the battery from draining. Third, instead of using a resistance box it is recommended to use the normal resistor in order to get the exact value of resistance and calculating the right value in the future.
Bibliography
Books
Hamper, Chris. Physics Higher Level. 2nd ed. Harlow: Pearson, 2014. Print
Pictures
“Commercial/industrial Energy Efficiency: Electric Cell – Internal Resistance of Battery.”Commercial/industrial Energy Efficiency: Electric Cell – Internal Resistance of Battery. N.p., n.d. Web. 22 Feb. 2017. <http://www.hk-phy.org/energy/commercial/act_int_resist_e.html>.