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

Electrical resistance is defined as the opposition to the flow of an electric current when it passes through a bulb or any other conductor.

• The SI unit of resistance is ohm (Ω).
• Every material has an electrical resistance, which is why conductors emit heat when current flows through them.
• Ohm's law states that the current flowing through a conductor is proportional to the potential difference across it.
• The potential difference between any two points is the amount of work done in transferring a unit positive charge without acceleration from one point to another along any path between the two points in the electric field.

Key Terms: Ohm’s law, Electrical resistance, Potential difference, Resistivity, Ammeter, Voltmeter, Rheostat, Specific resistance.

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Aim

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

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Apparatus Required

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• A wire of unknown resistance
• Milliammeter
• Battery
• Voltmeter
• Plug Key
• Rheostat
• Connecting wires
• Piece of sandpaper

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Circuit Diagram

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Circuit Diagram

Read Also: Uses of Resistor

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Theory

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According to Ohm’s law, the current flowing through a conductor is directly proportional to the potential difference at its ends, assuming the physical characteristics like temperature, dimensions, and pressure of the conductor remain constant.

If I is the current flowing through the conductor and V is the potential difference across its ends, then according to Ohm’s law

V ∝ I

And hence

V = RI

Where R is the proportionality constant and is known as the electrical resistance of the conductor. Resistance R is affected by the dimensions and material of the conductor. The formula expresses the relationship between a material's resistance and its length and area of cross-section is given by

R = ρ l/A

Where ρ is the specific resistance or resistivity of the conductor and is a property of the wire's material.

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Procedure

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1. Sandpaper should be used to remove any insulating layer from the connecting wire ends.
2. As indicated in the diagram, connect the resistance, rheostat, battery, key, voltmeter, and ammeter.
3. Check that the voltmeter and milliampere pointers line up with the zero mark on the measuring scale. If not, align the pointer with the zero mark by adjusting the screw at the base using a screwdriver.
4. Take note of the voltmeter and milliampere's range and least count.
5. Insert the key K and move the rheostat to the end where the current flow is minimum.
6. Take note of the voltmeter and milliampere readings.
7. Allow the wire to cool after removing key K. Insert the key again and move the rheostat slightly to increase the voltage. Take note of the milliampere and voltmeter readings.
8. Step 7 should be repeated four times for each rheostat adjustment. Create a tabular column to record the readings.

Read More: Electrostatic Potential

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Observations

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1. Length

Length of the resistance wire l = ……….

2. Range

Range of the given ammeter = ……….

Range of the given voltmeter = ……….

3. Least count

Least count of ammeter = ……….

Least count of voltmeter = ……….

4. Zero error

Zero error in ammeter, e₁ = ……….

Zero error in voltmeter, e₂ = ……….

5. Zero correction

Zero correction for ammeter, c₁ = – e₁ = ……….

Zero correction for voltmeter, c₂ = – e₂ = ……….

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Calculations

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1. As shown below, draw a graph between the potential difference across the wire V and the current I flowing through the wire.

2. Determine the slope of the graph. The resistance of the provided 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 = _____ Ω m^–1

Error Analysis

ΔR/R = ΔV/V + ΔI/I = ……

Where R is the resistance per unit length, and R indicates the expected error. V and I are the voltmeter and ammeter least counts, respectively.

Read more:

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Result

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1. The potential difference across the wire is proportional to the current.
2. The resistance per unit length of the wire is ( R ± ΔR) = _____ ± _____ Ω m^–1).

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Things to Remember

• The aim of this experiment is to determine the resistance per cm of a given wire by plotting a graph for potential difference versus current.
• The apparatus required to perform this experiment is a wire of unknown resistance, milliammeter, battery, voltmeter, plug key, rheostat, connecting wires, and piece of sandpaper.
• Ohm's law states that, under the assumption that the conductor's physical properties, such as its temperature, dimensions, and pressure, remain constant, the current flowing through a conductor is directly proportional to the potential difference at its ends.
• Connect the resistance, rheostat, battery, key, voltmeter, and ammeter as shown in the diagram.
• Take note of the voltmeter and milliampere readings.
• The result of this experiment is that the potential difference across the wire is proportional to the current.

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