Determining the resistivity of wires by plotting graph of  V-I

Objective:

To find the resistivity (ρ) of given wires by measuring their resistance (R) using Ohm’s law and then using the dimensions of the wire.

Apparatus Required:

Two or three different wires (e.g., copper, nichrome etc.)

An ammeter 0-3 A (to measure the current, I)

A voltmeter 0 to 3 V (to measure the potential difference, V)

A battery supply (battery Eliminator of 3A fuse and 2-12 volts selector switch)

A rheostat 2.3 A, 56 Ω (Variable resistor to control current)

A screw gauge (to measure the diameter of the wire)

A meter scale (to measure the length of the given wire)

Connecting wires (D.C.C copper)

One way Plug key

Experimental Setup:

Theory:

Ohm’s Law:

According to Ohm’s law, the potential difference (V) across a resistor is directly proportional to the current flowing through the resistor, provided the temperature remains constant.

V=IR Where

V – Potential difference (in volts, V)

I – Current (in amperes, A)

R – Resistance (in ohms, Ω)

The slope of V vs I graph gives the resistance R

Resistance and Resistivity:

The resistance R of a wire depends on

Its length (L)

Cross-sectional area (A)

Resistivity (ρ, a material property.

R=ρL/A

For a wire of diameter d, the area A

Resistance falls with thickness R ∝ 1/A and rises with length R ∝ l.

The amount that a material resist is determined by its resistivity, a material-dependent property.

Graphical Method:

Plotting V vs, I gives a straight line passing through the origin.

The slope of the graph gives resistance R =V/I

Using R, we can calculate the resistivity ρ=R A/L

 

Procedure:

Connect the ammeter in series with the circuit wire and the voltmeter in parallel with the wire.

Note the zero error of the metres.

Calculate the least count of the metres.

Switch on the circuit.

Set the rheostat to a particular position and record the readings of the ammeter and voltmeter.

Repeat steps 5 and 6 for different settings of the rheostat.

Repeat the procedure for second and third wires of different material.

Plot the graph: For each wire plot V (along Y-axis) vs, I (along X-axis)

Then calculate the resistivity of the individual wires.

For each wire find the resistivity using the formula

ρ=R A/L

How to find the least count of given ammeter and voltmeter?

Least count of Voltmeter:

Tabular Column & Observations:

Studying Ohm’s law with V-I Graph- Graphical method to find resistance

Studying Ohm’s law with V-I graph: Result

The V-I Graph is a straight line, verifying Ohm’s law.

The resistance(R) of the given resistor is found to be 3 Ω (From experiment)

The resistance(R) of the given resistor is found to be 3 Ω (From Graphical method)

How to find the radius of the given wire using a screw gauge?

Screw gauge:

Zero Error in Screw Gauge:

Positive Error in Screw Gauge

Negative error in Screw Gauge

Pitch of the Screw

Least Count of a Screw Gauge:

Diameter and Radius of a Wire:

Radius of the given wire: Tabular Column & Observations

Resistivity of the material of a wire – Calculations

Result:

The resistivity of the given first wire of resistance 2.919 Ω is =6.739×10^-7 Ωm

The resistivity of the given second wire of resistance 3 Ω is = ————– Ωm

The resistivity of the given third wire of resistance ——- Ω is =———– Ωm

Precautions:

Keep the temperature constant while finding the resistance of the wire.

Remove the plug key (switch off) when you are not taking the readings.

Always take multiple readings for accuracy.

Ensure tight connections to avoid contact resistance.

Viva Voce Questions:

1. State Ohm’s law.
2. Define resistivity. What are its unit
3. How does resistivity differ from resistance?
4. Why is rheostat is used? What happens if it is omitted?
5. Why is ammeter connected in series and the voltmeter in parallel?
6. What precautions are needed for wire connections?
7. What does the slope of the V-I graph represent? How do you calculate resistance from it?
8. Why should the V-I graph pass through the origin?
9. If the graph is non-linear, what could be the reason?
10. How do you find resistivity after determining R?
11. Why do we use thick wires in this experiment?
12. How does temperature affect resistivity? How does it impact your results?
13. What are the major sources of error in this experiment?
14. What is the reason for to measure the wire diameter at multiple points?
15. How would resistivity differ for wires of the same material but different lengths?
16. Can this method be used for liquids or semiconductors? Why/Why not?

Answers:

1. The current through a conductor is directly proportional to the potential difference across its ends, provided physical conditions remain constant.
2. It is the inherent property of a material that quantifies its resistance to electric flow. Unit: ohm-meter (Ω-m)
3. Resistance depends on dimensions (length, area) and material: resistivity is an intrinsic property of the material, independent of dimensions.
4. To vary the current in the circuit and to obtain multiple readings
5. Ammeter is a low resistance; measures current through the wire(series); voltmeter is of infinite resistance measures potential difference across it 9parallel)
6. Clean terminals, tight connections to avoid contact resistance, and minimal wire heating.
7. Slope of V/I= Resistance (R), R=slope = tan θ for the straight line
8. At V=0, I=0 (Ohm’s law for an ideal conductor)
9. Wire heating (resistance increases with temperature), non-ohmic material, or unstable connections.
10. Measure length (L), and diameter(d) of the wire: Calculate area(A) of wire and then use the resistivity formula.
11. Thick wires minimise temperature rise. Thin wires overheat quickly, altering resistance.
12. Resistivity increases with temperature for metals. Uncontrolled heating causes R to vary, leading to nonlinear graphs.
13. Inaccurate measurement of diameter | Contact resistance at terminals | Wire heating due to high current.
14. To check the uniformity and average variations, (wires may not be perfectly cylindrical)
15. Resistivity remains constant (material property). Resistance changes with dimensions but not the resistivity.
16. No, because they are non-linear, violating Ohm’s law.

Link to this experiment

‘RESISTIVITY OF THE MATERIAL OF A WIRE/PHYSICS PRACTICAL’

See more

The Resistivity of a Wire – A Comprehensive Guide

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