Determine Resistance Plotting Graph Potential Difference Versus Current

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What is Resistance?

The obstruction caused by the conductor to the current when the current flows through it is known as electrical resistance. Electrical resistance is offered by every material due to which materials become hot when current passes through them. The electrical resistance is the ratio of the voltage applied to the current that is flowing through an electric circuit. Wires also experience resistance, and in this article, we will learn how to determine resistance per cm of a given wire. 


Aim

The aim of this experiment is to determine resistance per cm of a given wire.


Materials Required

The items or materials required in this experiment are listed below.

  • A wire which has an unknown resistance

  • Battery

  • Voltmeter

  • Miliammeter

  • Rheostat

  • Plug key

  • Connecting wires

  • Piece of sandpaper


Theory 

According to Ohm’s law, the electric current that is meant to flow through the conductor is directly proportional to the potential difference that exists across the ends of the conductor, provided that the physical state of the conductor such as pressure, temperature, and dimension remains unchanged.

If I is considered as the electric current that is flowing through the conductor and Vis considered as the potential difference that exists across the ends of the conductor, then,

V  ∝ I

And hence,

V = RI

Where,

R is considered as the constant of proportionality and is termed as the conductor’s electrical resistance.

Resistance R  depends on the material used for the conductor and dimensions of the conductor. The relationship that exists between the resistance of a material and its length and area of the cross-section can be expressed by the below-given formula.

R = ρ(l/ A),

where ρ is considered as the specific resistance and resistivity, which is one of the characteristics of wire.

This above information is the theory that one should keep in mind before starting to determine resistance per unit length of a given wire. The experiment to determine resistance per cm of a given wire seems easy after understanding this above theory. The theory strengthens the base knowledge of the reader.


Procedure

The procedure to determine the resistance per unit length of a given wire goes as follows.

  1. The first step is to clean the ends of the connecting wire properly with the help of sandpaper which will remove the insulation coating that is present on the ends of the wire.

  2. Take the resistors, rheostat, battery, key, voltmeter, and ammeter, and connect all of them properly.

  3. Ensure that the pointers present in the voltmeter and milliammeter are coinciding with the zero mark of the measuring scale. If not, then adjust the screw present under by using a screwdriver to adjust the pointer so that it can coincide with the zero mark.

  4. It is important to ensure that the range and least count of the voltmeter and milliammeter are noted.

  5. Insert the key K and then slide the rheostat to the end where the current flow is minimum.

  6. The readings of the voltmeter and milliammeter are to be noted now.

  7. Remove the key K and let the wire cool for some time. After it cools down, again insert the key K and slightly increase the voltage by moving the rheostat then again note down the milliammeter and voltmeter reading.

  8. Repeat step 7 for four different rheostat adjustments and take down the reading of the voltmeter and the milliammeter in a tabular form.   

The above is the procedure one should follow to find resistance per cm of a given wire.


Observations 

The observations that are made in the process to determine the resistance per cm are as follows.

Length

Length of the resistance wire I = ……..


Range

Range of the given ammeter = ……

Range of the given voltmeter = ……


Least Count

Least count of ammeter = ……

Least count of voltmeter = ……


Zero Error

Zero error in ammeter, e₁ = ……..

Zero error in voltmeter, e₂ = …….


Zero Correction 

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

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


Calculations

Here we will discuss how to determine the resistance per cm of a given wire by plotting a graph, and the steps are as follows.

  1. Plot a graph between the potential difference across the ends of the conductor V and the current I.

  2. Then determine the slope of the graph, after which the resistance of the given wire will be the same as the reciprocal of the slope.

  3. The resistance of the wire as per unit length can be determined as = R / t = ____ Ωm-1.


Result

With the current, the potential difference across the wire ends also vary linearly. Thus, the resistance per unit length of the wire is ( R ± ΔR ) = ____  ±_____  Ωm-1.

FAQ (Frequently Asked Questions)

1. What Are the Factors That Resistance Depends On?

Resistance depends on the following factors:

  • Length = Length of the conductor is directly proportional to the resistance of the conductor.

  • Area = Cross-sectional area of the conductor is inversely proportional to the resistance of the conductor. It means that an increase in the cross-sectional area will cause a decrease in the resistance of the conductor.

  • Temperature = temperature of the conductor is directly proportional to the resistance of the conductor.

  • Resistivity = Resistivity of the conductor is directly proportional to the resistance of the conductor.

This can be expressed in the following formula.

R = (p*I) / A

2. What is Rheostat Used For?

Rheostat is an electronic device that acts as an adjustable component. Rheostats are required in experiments that require the adjustment of current or the varying resistance in an electric circuit. The rheostat is capable of adjusting generator characteristics, dim lights, and it can also start or control the speed of the motors. The resistance element of the rheostat is changed according to the application. Some of the resistance elements are metal wire or ribbon, carbon, or a conducting liquid.