Physics – Ohm’s Law Lab Report
Research Question
- To what extent is the Ohm’s Law true with specific regard to the
strength the correlation between current and voltage.
Overview
- The experiment that we have conducted was, made to check whether
the Ohm’s law can be replicated, and validate whether and when it
can be used in practical situations. Ohm’s law states that the voltage is
proportional to the current flowing through any conductor at a
constant temperature. Where the resistance remains constant.
Background Information
- Resistance (R) is calculated by V/I, Where V is voltage and I is current.
This means that when ‘V’ is increased ‘I’ will proportionally increase,
and when ‘V’ is decreased ‘I’ will proportionally decrease. But it only
applies to certain materials which are known as Ohmic resistors,
meaning that they follow Ohm’s law, while many others, like lamp
filaments, do not.
Apparatus
1. Ammeter – An Instrument for measuring electric current in amperes.
2. Voltmeter – An instrument for measuring electric potential in volts.
3. Rheostat – An electric instrument used to control a current by varying the
resistance.
4. Ohmic Resistors – Are those resistors that have constant resistance. In other
words, that follow the Ohm’s law. If you take such a resistor, apply voltage
across it, whilst measuring current and voltage, and then draw a graph of
current versus voltage, you get a straight line.
5. Switch – A device for making and breaking the connection in an electric
circuit.
6. Wires – Metal drawn out into the form of a thin flexible thread or rod
7. Battery Eliminator – Is any device which provides power to a circuit,
replacing the need or use of batteries.
Variables
Independent Variable – Current
Dependent Variable – Potential Difference across the resistor
Controlled Variables – Resistor, Components used in each trial and
Temperature.
Safety Precautions
- All components in this experiment are volatile and overheat extremely
quickly. Thus, improper handling can result in damage to both the
components and the user, as any mistake could lead to something
dangerous like the circuit catching fire and the user being burned, It is
essential that the temperature of the circuit is managed. Not only is it
important in terms of the effect on readings, but also that a sharp
increase in the temperature can result in shorting components, which
would lead to a fire and could cause harm to anyone near the
apparatus. Moreover it is necessary to make sure that the main switch
is turned off when connecting or dismantling the circuit, and all the
wires must be touched only using the insulation to avoid any chance of
electric shock.
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Circuit Diagram
Procedure
- Connect the circuit using the arrangement shown in the diagram
above. Although the original connection features a parallel connection
between the rheostat and the Ohmic resistor, it did not produce the
desired results, displaying unidentified anomalies, because of which
the positioning of the rheostat was switched to a series connection.
The battery eliminator’s EMF was set to 2 volts, because it would help
in measuring fine differences in the voltage when the resistance of the
rheostat is varied causing intervals of 0.1A. At every interval the
voltage was measured with 5 trials. The switched was inserted
momentarily, the reading of the voltmeter was quickly taken, and then
switch was removed. At this stage it is essential that parallax error is
avoided, so I made sure that my eye was in line with the hand and its
pivot, so that the measurement is accurate. After repeating this
procedure 5 times, the resistance of the rheostat would be reduced,
causing the total resistance to decrease, and therefore current in
series – total current – to increase, and the voltage in the resistor to
increase. 8 observations were taken from 0.1 – 0.8A, and was
recorded on a table.
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Data Collection
Legend
- V – Voltage (volts)
- I – Current (Amperes)
Calculating Averages
- After Calculating the mean for all the trials the table below was made.
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Uncertainities
Graphical Representation
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Findings and Calculations
The above graph is a Current-Voltage graph made using excel with current on
the x-axis and Voltage on y-axis. Since the characteristic of an Ohmic resistor
is 𝑉 ∝ 𝐼, I decided that the property can be best tested by auto-generating a
best fit line, and set one confirmed point at the origin. As seen on the graph,
I have generated error bars with a fixed value of 0.025 Amps or Volts, while
percentage uncertainties are irrelevant due to both the values being
measurements that I took directly from the circuit components. As displayed
on the graph, the best fit line passes through the origin and has a an equation
𝑏𝑦 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛
of 𝑦 = 1.1676𝑥 ∴ 𝑉 = 1.1676𝐼 ⇒
1.1676 =
𝑉
𝐼
=𝑅
Thus, the best fit line’s gradient is equal to the combined resistance of the
resistor and voltmeter. Even with the rest of the circuit being connected in
series, the voltmeter is connected in parallel, and it has a very high resistance
(not infinite), which causes the resistance that is found to slightly change. This
can be shown using the formula below:
1
1
1
=
+
𝑅
𝑅1 𝑅𝑉
Here R1 is the resistance of the ohmic resistor, while RV is the resistance of the
voltmeter. Since we already know the combined resistance of the resistor and
voltmeter using the graph’s best fit line, we can calculate the resistance of the
voltmeter. Moving on to the uncertainty in the gradient itself. We can
calculate the uncertainty in the gradient, i.e. the value of resistance found
using the graph. It can be calculated by finding out the values of resistance at
the points that are situated either at the bottom-right, or top-left corner of
the square shaped areas created by the error bars on the graph for the first
and last data point, which can then be used to find maximum and minimum
gradient.
𝑀𝑎𝑥. 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
(0.9 + 0.025) − (0.1 − 0.025)
= 1.30769 … ≈ 1.31
(0.8 − 0.025) − (0.1 + 0.025)
𝑀𝑖𝑛. 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
6
(0.9 − 0.025) − (0.1 + 0.025)
=1
(0.8 + 0.025) − (0.1 − 0.025)
∴ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
1.31 − 1
0.31
=
= 0.155
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Evaluation
Although most procedures were carefully carried out, this experiment has
one significant systematic error. As it can be seen the resistance is shown as
1.1676Ω, which is higher than the marked resistance of 1Ω. When resistors
are connected in parallel, in this case the resistor and voltmeter, the
combined resistance is always lower than the individual resistance of either
of the resistors. This means that there was a systematic error when collecting
data. One of the most crucial variables that need to be controlled in this
experiment is temperature. Ohm’s law is only valid for a conducting material
at constant temperature. When the temperature changes, the resistance also
changes, causing the values to change throughout the entire experiment. As
it can be seen from the data points in the graph, the value for resistance is
low initially, then increases, and then continues to decrease. The reason for
this error is that when the measurements were taken and the switch was
removed, the next measurements were almost immediately taken, which
meant that the temperature was not allowed to return to the initial level,
causing the resistance to constantly change throughout. Moreover, the time
of wait before inserting the switch back was not uniform, which meant that
the temperatures were almost always different, making most of the values
inaccurate. This factor is also somewhat subject to random error, as the
temperature of the environment may also constantly change, although the
laboratory was an air-conditioned room, which controls the temperature
mostly. The disparity in temperature can be reduced by letting the circuit
remain open for about 1 minute before re-inserting the switch, so that the
circuit’s temperature would be close to that of the room. Moreover, there
was an incident where one of the wires broke, upon which it was replaced,
but the readings were not re-started from the beginning, but continued from
where it was, adding on to the systematic error of the experiment. The
random error is mostly reduced because averages of 5 trials across 8 different
observations were taken, yet there is an improvement that can be made to
reduce it even further. As seen in table 3, the fractional/percentage
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continuously reduces as the voltage increases, since the absolute uncertainty
is constant. Since the values are used in further calculations, like division to
find out resistance, the uncertainty will carry over to the new values found
using it. Thus, it is beneficial to use higher intervals, for eg. 0.2 A each, to make
the readings of current and voltage higher, where the random error will not
affect the final value as much as it does when smaller values are used. By
making the above changes to the experiment, the readings observed will be
more accurate and uniform.
Bibiliography
Tsokos, K.A. Physics for the IB Diploma. Cambridge University Press, 2014.
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