finding the resistance of a wire experiment

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Lab Report Explained: Length and Electrical Resistance of a Wire

• Lab Report Explained: Length and…

INTRODUCTION AND BACKGROUND THEORY

When electrons travel through wires or other external circuits, they travel in a zigzag pattern that results in a collision between the electrons and the ions in the conductor, and this is known as resistance. The resistance of a wire causes difficulty for the flow of the electrical current of a wire to move and is typically measured in Ohms (Ω).

George Ohm discovered that the potential difference of a circuit corresponds to the current flowing throughout a circuit and that a circuit sometimes resists the flow of electricity. The said scientist hence came up with a rule for working out resistance, shown on the image on the side:

Resistance is an important factor to pay attention to because, one, an overly-high resistance can cause a wire to overheat due to the friction that is caused when the electrons move against the opposition of resistance, which is potentially dangerous as it could melt or even set fire. It is therefore important to take note of the resistance when dealing with wires to supply power to a device or so.

A real life application would be a toaster where the wires are sized to get hot enough to toast bread but not enough to melt.

Secondly, resistance can also be used a very useful tool that enables you to control certain things. An example from the real-life world would be LED lights that require a resistor to control the flow of the electrical current to prevent getting damaged by high electrical current. Another example would be the volume control on a radio where a resistor is used to portion out the signal, which allows you to control the volume level.

It is clear now that resistance is an important attribute that has been applied to many forms of technology to perform a useful function, and this experiment aims to see how we can control it. The resistance of a wire varies according to the four factors of the wire; are temperature, material, diameter/thickness, and length of the wire.

This experiment will be focusing specifically on that last factor – length – and investigate just how much of a role a length of a wire would have on its electrical resistance by using a range of wire lengths to test with.

RESEARCH QUESTION

How does changing the length of a nichrome wire with a diameter of 0.315 mm – cut into measurements of 10cm, 20cm, 30cm, 40cm and 50cm — affect the electrical resistance generated within the nichrome wires that can be captured by an ohmmeter while keeping the temperature and the location of the experiment controlled?

If the length of nichrome wire is increased by an increment of 10cm starting from 10cm in length, then the graph measuring the electrical resistance of the wires will observe a positive slope with the mathematical function of y = mx that displays the increasing amount of resistance generated.

REASON FOR HYPOTHESIS

Doubling a length of a wire is just like having two of the shorter wires in series. If one short wire has a resistance of 1 ohm, then 2 shorts wires would have a resistance of 2 ohms when connected in series.

A longer wire also means that it would have more atoms, which means it will be more likely for moving electrons to collide with them; hence, higher resistance. For instance, a 10cm wire has 5 atoms, a 20cm wire has 10 atoms. If say 5 electrons try to pass through those two wires, the chances of them bumping into atoms are higher in the 20cm wire than the 10cm one. Therefore, the longer the wire, the higher the resistance.

Source: “Resistance” Physics Classroom. The Physics Classroom, n.d. Web. May 8. 2018. [http://www.physicsclassroom.com/class/circuits/Lesson-3/Resistance]

MATERIAL AND APPARATUS

Experiment design setup with clear labels.

• Put on safety goggles, lab coats, gloves and masks for safety.
• Handle all materials carefully.
• Have a clear and clear working space for the experiment.
• Do not consume any of the materials used, and keep them away from the eyes.
• Complete all trials in the same area/room, at the same time of the day, using the same materials.
• Clean up the lab area after the experiment.
• Wash all materials thoroughly with warm water and soap after the experiment.

EXPERIMENT METHOD/PROCEDURE

• Gather materials and set up the circuit as shown in the experiment diagram above.
• Set the multimeter into ohmmeter, and connect the red probe to the output that says COM and the black probe to the output that has the mAVΩ label.
• Get 150cm of nichrome wire and scrap or rub it with sandpaper in order to make it conductive.
• Cut the wire with scissors into 5 separate wires with measurements of 10, 20, 30, 40 and 50cm.
• Measure each wire by putting the points of both probes to the edges of the wires, and measure them four times/trials each.
• Record the resistance reading from the multimeter of each of the 5 wires.

Recorded Resistance for 5 Different Lengths of Nichrome Wire

SAMPLE CALCULATION OF PROCESSED DATA

Average data no. 3: (6.50+7.00+6.50+7.90) ÷ 4 = 6.98 Average uncertainty data of no. 3: (7.90-6.50) ÷ 2 = 0.70

GRAPH (based on average data)

CONCLUSION & EVALUATION

The graph shows an increasing linear trend-line with the mathematical function of Y = 0.132X + 2.3, which displays a positive correlation as seen in the line that goes above and to the right, which indicates positive values, as well as the gradient that displays a positive value. The graph also has an identified slope or gradient of 0.132.

This unit for this gradient is ohm/cm, and the gradient represents the rate of the overall increase in the dependent variable as the independent variable progresses. The slope reveals that when the length of a wire is increased, the resistance would go up by an approximate measurement of 1.25 Ω, which could be proven by the calculation of the graph where all the average was calculated from the average increments of each wire — (0.7+0.78+2.42+1.1)÷4=1.25.

Another aspect from the mathematical function that can be identified is the Y intercept which was 2.3, and it represents the average resistance (dv) of the first data of the independent variable, which was 3.48 Ω.

The data for the length of wires (independent variable) was 10cm to 50cm with an increment of 10cm between each wire, while the resistance (dependent variable) seemed to display the lowest data of 3.48 Ω and the highest data of 8.48 Ω, which seems to fit well with modeled best fit line graph, which is visibly supported by the coefficient determination (R2) which states that the best-fit line fits the scattered data by 94.98%

The data does not perfectly fit the modeled best fit line as errors did occur along with the experiment, as displayed by the rather large error bars over the data. The maximum error bar that can be identified there is the 4th independent variable, which was the 40cm wire, and the minimum error bar was located in the 1st data, which was the 10cm wire.

Two data of the largest errors went way above the predicted line, which from it we can infer that the collected data is considered to have an inconsistent precision. When coming to measure those two data, the data gained from each trial were very inconsistent, which was presumably caused by the inconsistent rubbing with sandpaper, which will be further elaborated in the suggestions for improvements.

The pattern on the graph supports the hypothesis of the experiment which predicted that if the length of the wire increased, the resistance measured would increase as well, the graph will observe a positive gradient with the mathematical function of y = mx + c which is supposed to display the increasing amount of resistance.

This was proven and supported by the trend-line in the graph which basically shows a positive correlation in the increase in resistance at the same rate as the independent variable increases, which is just as the hypothesis predicted. The graph also manifested a positive mathematical function of y = 0.132x + 2.3 with a positive gradient (0.132x) as well.

There is, however, a scientific explanation behind all this. It has been a known fact that the length of a wire is one of the four factors that have a role in the resistance of the wire, and this experiment has simply confirmed it.

The logical explanation would be that a longer wire also means that it would have more atoms, which means it will be more likely for moving electrons to collide with them; hence, higher resistance. For instance, a 10cm wire has 5 atoms, a 20cm wire has 10 atoms. If say 5 electrons try to pass through those two wires, the chances of them bumping into atoms are higher in the 20cm wire than the 10cm one. Therefore, the longer the wire, the higher the resistance.

In conclusion, the experiment was a successful investigation that successfully answers the research question of how basically changing the length of a wire (especially a nichrome wire with a diameter of 0.315 cut into measurements of 10cm, 20cm, 30cm, 40cm and 50cm) could affect the electrical resistance generated within the wires.

The investigation has concluded that there is a clear relationship between the length and the resistance of a wire and that the former does in fact affect the latter.

EVALUATION AND SUGGESTIONS

BIBLIOGRAPHY

• “Potential Difference” BBC – GCSE Bitesize. BBC, Sep 15. 2006. Web. May 8. 2018. [http:// bbc.co.uk/schools/gcsebitesize/design/electronics/calculationsrev1.shtml]
• “Resistance” Physics Classroom. The Physics Classroom, n.d. Web. May 8. 2018. [http:// physicsclassroom.com/class/circuits/Lesson-3/Resistance]
• “Resistance and Resistivity” N.p., n.d. Web. May 8. 2018. [http://resources.schoolscience.co.uk/CDA/16plus/copelech2pg1.html]
• “Resistance: Chapter 1 – Basic Concepts of Electricity” All About Circuits. EETech Media, LLC, n.d. Web. May 8. 2018. [https://www.allaboutcircuits.com/textbook/direct-current/chpt-1/resistance/]

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excellent work. thank you ever so much.

Glowing regards, Shan

Data analysis?

indeed a great help

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To find resistance of a given wire using Whetstone’s bridge (meter bridge)

To find resistance of a given wire using Whetstone’s bridge (meter bridge) & hence determine the specific resistance of the material.

A meter bridge (slide Wire Bridge), a galvanometer, a resistance box, a laclanche cell, a jockey, a one- way key, a resistance wire, a screw gauge, meter scale, set square, connecting wires and sandpaper.

Formulae Used:

(i) the unknown resistance x is given by:.

X= (100-ι)/ιx R where

R = known resistance placed in left gap.

X = Unknown resistance in right gap of meter bridge.

ι=length of meter bridge wire from zero and upto balance point (in cm)

(ii) Specific resistance (ρ) of the material of given wire is given ρ = XπD 2 /4L

D: Diameter of given wire L: Length of given wire.

Observation Table for length (ι) & unknown resistance, X:

Table for diameter (d) of the wire:, circular scale reading, observations:.

• Least count of screw gauge: 0.001 cms
• Pitch of screw gauge: 0.1 cm
• Total no. of divisions on circular scale: 100
• Least Count =Pitch/No. of divisions on circular scale; LC = 0.001 cm
• Length of given wire, L = 25cm

Calculation:

For unknown resistance, X:

Mean X = X 1 X 2 + X 3 + X 4 / 4 = 2.68Ω

Mean diameter, D= D 1 D 2 + D 3 + D 4 / 4 =0.035cm

Specific Resistance, ρ= X.πD 2 /4L=1.03 x 10 -4 Ωcm

Value of unknown resistance = 2.68Ω

Specific resistance of material of given wire = 1.03 x 10 -4 Ωcm

Precautions:

All plugs in resistance box should be tight. Plug in key, K should be inserted only while taking observations.

Sources of Error:

• Plugs may not be clean.
• Instrument screws maybe loose.

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Related categories.

• Class 12 Physics
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Class 12 Physics Lab Experiment list

• 1 To find resistance of a given wire using Whetstone’s bridge (meter bridge)
• 2 To find the focal length of a convex mirror using a convex lens
• 3 To find the value of ‘v’ for different values of ‘u’ in case of a concave mirror & to find its focal length
• 4 To draw the characteristics curves of a zener diode vs to determine its reverse breakdown voltage
• 5 To verify the laws of combination (series & parallel) of resistances using meter bridge (slide Wire Bridge)
• 6 To determine the internal resistance of a primary cell using a potentiometer
• 7 To find the focal length of a convex lens by plotting a graph

Laboratory Experiment Categories

• Electrical and Electronics
• Civil Engineering
• Engineering Mechanics
• Mechanical Engineering
• Biomedical Engineering

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Verification of Ohm’s Law experiment with data and graph

In the previous article, we discussed Ohm’s Law of current electricity. In this article, we’re going to perform an experiment for the verification of Ohm’s law. This practical verification of Ohm’s law is very important for the students of grades 10 and 12. This is a lab-based experiment to verify Ohm’s law or Ohm’s law practical.

Aim of the Experiment

Aims of the ohm’s law experiment are as followings –

• Verification of Ohm’s Law by showing that the Voltage to Current ratio is constant.
• To determine the resistance of a wire by plotting a graph for potential difference (V) versus current (I) using Ohm’s Law.
• To find the resistivity of a wire by plotting a graph for potential difference versus current.

Theory of the Ohm’s law experiment

From Ohm’s law , we know that the relation between electric current and potential difference is V = IR

or, \color{Blue}R=\frac{V}{I} ………….. (1)

Where I is current, V is the potential difference and R is the resistance.

Again, the formula for the resistance of a wire is, \color{Blue}R=\frac{\rho L}{A}

or, resistivity, \color{Blue}\rho = \frac{RA}{L} ………. (2)

Where A is the cross-section area of the wire. A = πr 2 where r is the radius of the wire. L is the length of the wire.

In this experiment, we will find the current and the potential difference across the sample wire by using Ammeter and Voltmeter respectively. Then the resistance of the wire can be found by using equation (1).

Again, We have to take at least five sets of data for different voltages and currents. Then a graph is needed to plot the current along the positive Y-axis and the potential difference along the positive X-axis.

• Ohm’s Law can be verified by finding the Voltage to current ratio. If the ratio remains constant [equation- (1)] for all sets of data, then we can say that the voltage across the resistance is proportional to the current through it which is nothing but Ohm’s Law.
• One can easily find the value of resistance of the wire from the slope of the graph. R = \frac{V}{I}
• One can find the resistivity of the wire from equation (2) by using the value of R from the graph. Usually, the examiner supplies the radius (r) or diameter (2r) and length (L). If radius and Length are not given then we have to find those by using a screw gauge and meter scale respectively.

Apparatus Used

The apparatus used for this experiment –

• A power supply (Voltage source or Battery): The used battery can supply the voltage from 0 to 12 volts.
• An Ammeter (A) to measure current. This Ammeter can measure the current from 0 to 3 amperes.
• A Voltmeter (V) to measure Voltage. The used Voltmeter can measure the voltage from 0 to 3 volts.
• A rheostat controls and adjusts the current through the circuit.

Circuit Diagram

Fig. (1) gives the circuit diagram for the verification of Ohm’s Law lab experiment.

Here, R is the resistance of the wire, A is the ammeter, V is the Voltmeter, Rh is the rheostat and K is the key. The arrow sign indicates the direction of the current flow in the circuit .

Formula used for the Ohm’s law lab experiment

The formulae used for the Ohms law lab work are

\color{Blue}R = \frac{V}{I} ………….. (1) and \color{Blue}\rho = \frac{RA}{L} ………. (2)

Experimental data

The least count of Ammeter = Smallest division of Ammeter = 0.05 ampere

The least count of Voltmeter = Smallest division of voltmeter = 0.05 Volt

So, we can see that in each observation the voltage-to-current ratio is almost the same. Thus, the voltage across the wire is proportional to the current through the wire. Hence Ohm’s law is verified .

Now we got the calculated value of the resistance of the wire is R = 1.02 ohm.

We also need to plot I-V graph to confirm the experimental value of R.

Current versus Voltage graph (Ohm’s Law graph)

If we plot the Current as a function of voltage with the help of the above data then we will get a straight line passing through the origin.

Calculations

Calculation of resistance from the graph.

The inverse of the I-V graph gives the resistance of the wire. Now, from the graph, change in current, ∆I = AB = 0.5 amp corresponding change in voltage, ∆V = BC = 0.5 volt Thus, the Resistance from the graph, R = ∆V/∆I = 0.5/0.5 = 1.00 ohm

Calculation of resistivity of the wire

Length of the wire is, L = 50 cm = 0.5 m Radius of the wire. r = 0.25 mm = 0.25 × 10 -3 m So, the cross-section area of the wire, A = πr 2 = 3.14 × (0.25×10 -3 ) 2 = 0.196 × 10 -6 m 2 Thus from the equation-2 we get the resistivity of the material of the wire is, \rho = (1 × 0.196 ×10 -6 )/0.5 or, \rho = 0.392 × 10 -6 = 3.92 ×10 -7 ohm.m Thus the resistivity of the material of the wire is 3.92 ×10 -7 ohm.m

Final result

The resistance of the wire from the Current-Voltage graph is, R = 1.00 ohm The calculated value of the resistance of the wire is, R = 1.02 ohm. Resistivity of the material of the wire is 3.92 ×10 -7 ohm.m

Discussions

• When the voltage V = 0, the reading of the ammeter is zero. That means the current through the wire is zero. Now, one cannot calculate the resistance for this data because one cannot measure the opposition faced by the current until the current flows.
• In the last two data, the current has not increased as much as first three observations. This is because of the increase in resistance of the wire due to heating. Here current flow through the wire causes joule’s heating.
• The calculated value of resistance almost matches the resistance calculated from the graph.
• If the radius (r) and length (L) of the wire are not supplied, then we have to determine those parameters by screw gauge and the meter scale respectively.
• In this experiment 1) verification of ohm’s law is done 2) Unknown resistance of the wire and 3) Resistivity of the material of the wire is determined.

This is all from this post on experimental verification of ohm’s law. If you find this post helpful, share it with your classmates and friends.

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• CBSE Class 12
• CBSE Class 12 Physics Practical
• Determine Resistance Plotting Graph Potential Difference Versus Current

To Determine Resistance per CM of a Given Wire by Plotting a Graph for Potential Difference versus Current

We know that resistance is a measure of the opposition to the flow of electricity in a circuit. The potential difference helps to understand the amount of energy transferred between two points in a circuit. In this session, let us learn to determine the resistance per cm of a given wire by plotting a graph for potential difference versus current.

To determine the resistance per cm of a given wire by plotting a graph for potential difference versus current.

Apparatus/Material Required

• A wire of unknown resistance
• Milliammeter
• Connecting wires
• Piece of sandpaper

Circuit Diagram

According to Ohm’s law, the electric current flowing through a conductor is directly proportional to the potential difference across its ends, provided the physical state (pressure, temperature, and dimensions) of the conductor remains unchanged.

If I is the current flowing through the conductor and V is the potential difference across its end, then

Where R is the constant of proportionality and is termed as the electrical resistance of the conductor. Resistance R depends on the dimensions and material of the conductor. The relationship between the resistance of a material and its length and area of the cross-section is given by the formula

Where ρ is the specific resistance or resistivity and is a characteristic of the material of the wire.

• Clean the ends of the connecting wire with the help of sandpaper to remove any insulating coating on them.
• Connect the resistance, rheostat, battery, key, voltmeter, and ammeter as shown in the figure.
• Make sure that the pointers in the voltmeter and milliammeter coincide with the zero mark on the measuring scale. If not, adjust the pointer to coincide with the zero mark by adjusting the screw provided at the base using a screwdriver.
• Note the range and the least count of the given voltmeter and milliammeter.
• Insert the key K and slide the rheostat to the end where the current flow is minimum.
• Note the voltmeter and the milliammeter reading.
• Remove the key K and allow the wire to cool. Again insert the key and slightly increase the voltage by moving the rheostat. Note down the milliammeter and voltmeter reading.
• Repeat step 7 for four different adjustments of the rheostat. Document the readings in a tabular column.

Observations

Range of ammeters = _____ mA to _____ mA

The least count of ammeter = _____ mA

Range of voltmeter = _____ V to ____ V

The least count of voltmeter = _____ V

The least count of meter-scale = _____ m

Length of the given wire, l = _____ m

Calculations

• Plot a graph between the potential difference across the wire V and the current I flowing through the wire as shown below.

2. Determine the slope of the graph. The resistance of the given wire is then equal to the reciprocal of the slope.

From the graph, R = BC / AB = _____ Ω

3. Resistance per unit length of the wire = R/t = _____ Ωm –1

Here, R is the resistance per unit length and Δ R is the estimated error. Δ V  and Δ I are the least count of voltmeter and ammeter respectively.

The potential difference across the wire varies linearly with the current.

The resistance per unit length of the wire is ( R ± Δ R ) = _____ ± _____ Ωm –1 ).

1. State Ohm’s Law.

Ohm’s law states that the potential difference across an ideal conductor is proportional to the current through it. The constant of proportional is known as the resistance R . Ohm’s law is given by V = IR .

2. Which are the factors on which the resistance of a conductor depends on?

The resistance of a conductor depends on the following factors:

• Resistivity
• Temperature
• Cross-sectional area

3. What is a rheostat?

A rheostat is a variable resistance that is used to control the current.

4. What is the shape of a V vs I graph for a linear resistor?

The shape of the V vs I graph for a linear resistor is a straight line.

5. What is the reciprocal of resistivity called?

The reciprocal of resistivity is called conductivity.

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