Step-by-Step Guide to Drawing and Interpreting V-I Graphs
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.
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.
Take the resistors, rheostat, battery, key, voltmeter, and ammeter, and connect all of them properly.
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.
It is important to ensure that the range and least count of the voltmeter and milliammeter are noted.
Insert the key K and then slide the rheostat to the end where the current flow is minimum.
The readings of the voltmeter and milliammeter are to be noted now.
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.
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.
Plot a graph between the potential difference across the ends of the conductor V and the current I.
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.
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.
FAQs on How to Determine Resistance by Plotting Potential Difference vs Current
1. How can you determine the resistance of a wire by plotting a graph of potential difference versus current?
To determine resistance from a V-I graph, you follow these steps:
Set up a circuit containing the resistance wire, a battery, an ammeter (in series), a voltmeter (in parallel with the wire), and a rheostat.
Adjust the rheostat to get several different values for current (I) and measure the corresponding potential difference (V) across the wire for each.
Plot a graph with potential difference (V) on the y-axis and current (I) on the x-axis.
The graph should be a straight line passing through the origin, which verifies Ohm's Law.
Calculate the slope of this line (ΔV/ΔI). This slope directly gives the value of the resistance (R) of the wire.
2. What does the graph of potential difference (V) versus current (I) represent for an ohmic conductor?
For a conductor that obeys Ohm's Law (an ohmic conductor), the graph of potential difference (V) versus current (I) is a straight line that passes through the origin. This linear relationship shows that the potential difference is directly proportional to the current. The slope of this V-I graph represents the constant resistance (R) of the conductor.
3. What are the key factors that the electrical resistance of a conductor depends on?
The electrical resistance (R) of a conductor is determined by four main factors:
Length (L): Resistance is directly proportional to the length of the conductor. A longer wire has more resistance.
Cross-sectional Area (A): Resistance is inversely proportional to the cross-sectional area. A thicker wire has less resistance.
Temperature: For most metallic conductors, resistance increases as the temperature rises.
Material (Resistivity, ρ): The intrinsic property of the material, known as resistivity, determines its resistance. Materials like copper have low resistivity, while materials like nichrome have high resistivity.
4. What is the specific function of a rheostat in the experiment to determine resistance?
A rheostat acts as a variable resistor in the circuit. Its primary function is to systematically change the total resistance of the circuit, which in turn varies the current (I) flowing through the resistance wire. By adjusting the rheostat, you can obtain a range of different current and voltage readings needed to plot an accurate V-I graph, rather than relying on a single measurement.
5. Why is it better to plot a graph to find resistance instead of calculating it from a single V/I reading?
Relying on a single measurement of voltage (V) and current (I) is highly susceptible to random errors, such as parallax error in reading the meters or slight fluctuations in the power supply. By taking multiple readings and plotting a V-I graph, you can draw a best-fit line that averages out these random errors. The resistance calculated from the slope of this line is a much more accurate and reliable representation of the true resistance.
6. What is the difference between resistance and resistivity, and how can resistivity be found from this experiment?
Resistance (R) is the opposition to current flow for a specific object and is measured in Ohms (Ω). It depends on the object's dimensions (length and area). Resistivity (ρ), on the other hand, is an intrinsic property of the material itself, indicating how strongly it resists current flow, and is measured in Ohm-metres (Ωm). After finding the resistance (R) from the V-I graph, you can determine resistivity by measuring the length (L) and cross-sectional area (A) of the wire and using the formula: ρ = (R × A) / L.
7. What would happen to the V-I graph if the temperature of the wire increases significantly during the experiment?
If the temperature of the wire increases, its resistance will also increase. As a result, the V-I graph will no longer be a perfect straight line. It will start to curve upwards, bending away from the current (I) axis. This is because for the same increase in voltage, the current will increase by a smaller amount due to the higher resistance. The conductor would begin to exhibit non-ohmic behaviour.
8. If you accidentally plot current (I) on the Y-axis and potential difference (V) on the X-axis, how would you calculate resistance from the slope?
If the axes are swapped, the slope of the graph would be ΔI/ΔV. According to Ohm's Law, resistance R = V/I. Therefore, the slope (ΔI/ΔV) is equal to 1/R. To find the resistance in this case, you would need to calculate the reciprocal of the slope. So, R = 1 / slope.
