To Determine Resistance Per cm of a Given Wire by Plotting a Graph of Potential Difference Versus Current

A conductor is made of infinite atoms, each of these have a nucleus as well as orbiting electrons. When an external field is applied to these electrons, they drift leading to the origin of current. When these electrons encounter heavy nuclei, they collide and slow down. This opposition to current is called resistance $(R)$. The resistance is represented by the formula $R \ = \ \rho \frac{L}{A}$ where, $\rho$ is specific resistance which depends only on the material of the conductor and $L$ is length whereas $A$ is cross-section area which define the dimensions of the conductor.

It also changes with change in temperature. It increases with temperature and can be predicted by the formula $R_T \ = \ R_0 [1 \ + \ \alpha \Delta T]$ 

Where, $R_T$ is resistance at given temperature, $R_0$ is resistance at absolute zero, $\alpha$ is the temperature coefficient and $\Delta T$ is the change in temperature.

Table of Contents

1. Aim

2. Apparatus required

3. Theory 

4. Procedure

5. Observations 

6. Result

7. Precautions

8. Lab Manual Questions 

9. Viva Questions 

10. Practical Based Questions 

Aim

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

Apparatus Required

• Wire of unknown resistance $(\sim 10 \Omega)$

• Battery eliminator or an accumulator $(0 \ - \ 3V)$ or two dry cells $(1.5 V \ each)$ 

• Voltmeter $(0 \ - \ 5 V)$

• Milliammeter $(0 \ – \ 500 mA)$

• Rheostat

• Plug key

• Connecting wires

• Piece of sandpaper

Theory

According to Ohm's law, if a conductor's physical state doesn't change, the electric current flowing through it is directly proportional to the potential difference at its ends.

If $I$ is the current flowing through a conductor due to a potential difference $V$ applied across its ends, then by Ohm’s law we have:

$V\propto I$

And hence, $V=RI$ …..(1)

Where, $R$ is the constant of proportionality, known as the electrical resistance of a conductor. It is the opposition to the flow of electrons in a conductor, due to the presence of constituent atoms. $R$ is represented in ohms $(\Omega)$ if $V$ is expressed in volts and $I$ in Amperes. The conductor's material and dimensions have an impact on the resistance $R$. The resistance for a wire with a uniform cross section relies on the length $l$ and the cross-sectional area $A$. The conductor's temperature is another factor. The resistance at a particular temperature can be represented by 

$R \ = \ \rho \times \frac{l}{A}$ …..(2)

Where, $\rho$ is specific resistivity and depends on the material of the conductor. 

Using (1) and (2), we have,

$V \ = \ \left ( \rho \frac{l}{A} \right ) \times \ I$ …..(3)

Comparing (3) with equation of graph with straight line slope $y = mx$ we can deduce that if a graph of $V$ versus $I$ is plotted, with $V$ on the y-axis and $I$ on the x-axis, then the slope of the graph will give the value of resistance $R$.

Procedure

1. With the use of sandpaper, clean the connecting wires' ends to remove any insulating coating.

2. Connect the circuit as shown in the diagram. 

Circuit diagram

3. Adjust the voltmeter and milliammeter such that their needles coincide with the zero mark. This will ensure error free reading.

4. Slide the rheostat contact to one of its extreme ends, after inserting the key $K$, to ensure that the least amount of current is going through the resistance wire. Now note the readings of the voltmeter and the milliammeter.

5. Unplug the key $K$ and wait for the wire to cool. Shift the rheostat to decrease resistance and increase potential applied. Now plug in the key $K$ and note the new voltmeter and milliammeter readings.

6. Repeat the above step at least four times, with different rheostat settings and note the readings each time.

Observation

Ammeter range- 

Least count of ammeter-

Range of voltmeter-

Least count of voltmeter- 

Length of the given wire-

Least count of meter scale-

Observation Table

Result

• Plot a graph between $V$ and $I$, with $V$ on the y axis and $I$ on the y axis. By Ohm’s law, the slope of the graph will give value of resistance of wire $R$

Graph for Ohm’s law

• With the help of length of wire $l$, we can calculate resistance per centimeter by $\frac{Resistance \ (R)}{Length \ of \ wire \ (l)}$

• Error in reading:

$ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I}$

• Therefore, 

The resistance of the wire is 

The error in measurement is 

The resistivity of the wire is 

Precautions

• The circuit should have the voltmeter connected in parallel and the ammeter connected in series.

• Make sure that the positive terminal is where current enters and the negative terminal is where it exits.

• The key should only be inserted when making observations since a high current flowing through will heat the wire unnecessarily and alter its resistance.

• It is important to be aware of and eradicate any measurement equipment of zero error, including voltmeters, ammeters, and meter scales. Voltmeters and ammeters may be adjusted by turning the screw at the base of the needle with the use of a screwdriver.

Lab Manual Questions

1. It is said to always connect an ammeter in series and a voltmeter in parallel with the circuit. Why? If connected in a reverse arrangement, will they still give correct readings?

Ans: The ammeter reads the current whereas the voltmeter reads the voltage. The current for two electrical elements in series is the same, therefore the ammeter must be connected in series. Similarly, the voltmeter is connected in parallel since two electrical elements connected in parallel have the same potential difference across their ends. If they are connected in reverse arrangement, they won’t give correct readings.

2. Why are copper wires typically used to connect various electrical circuit components?

Ans: Copper is an excellent conductor of electricity. Therefore, it is used to make connecting wires to minimize resistance through the circuit.

3. How does the length of wire affect its resistance, when its diameter is kept constant?

Ans: The resistance is represented by the formula $R \ = \ \rho \frac{L}{A}$ where, $\rho$ is specific resistance which depends only on the material of the conductor and $L$ is length whereas $A$ is cross-section area which define the dimensions of the conductor.

Therefore, if the diameter is kept constant, $A$ becomes constant. The relation between resistance $R$ and length $l$ hence becomes direct.

4. What happens if the circuit is left with the current flowing continuously for a prolonged period? Why?

Ans: If the circuit is left with the current flowing continuously for a prolonged period, the current flowing through wires produces heat and increases their temperature. Due to this, the resistance of wire also increases.

Viva Questions

1. The length of two identical wires made of the same material is the same. While the other has a non-circular cross section of the same area A, the first has a circular cross section of that area. Will they have comparable resistances?

Ans: They will have the same resistances irrespective of the shape of the cross section.

2. What are the possible sources of error?

Ans: Few possible sources of error include:

1. The cross-sectional area of the wire may not be uniform.

2. The resistance wire's length should be measured between the voltmeter's two terminals. If included, the lengths of ends looped around the voltmeter's terminals would introduce measurement error.

3. The wires are heated and thus provide some resistance.

3. What is the use of a rheostat in the circuit?

Ans: It is used to vary the resistance in the circuit and obtain multiple readings for the same set up.

4. Why is the voltmeter connected in parallel?

Ans: This is because it measures potential difference and the potential difference across to points in parallel is the same.

5. What factors affect the resistance of a conductor?

Ans: The resistance of a conductor is dependent upon its length, cross-section area, its material and temperature.

6. How does resistance vary with temperature for conductors and semiconductors?

Ans: The resistance of a conductor increases with temperature ohmically whereas it decreases for the semiconductor up to a certain point, with increase in temperature.

7. Why is the ammeter connected in series?

Ans: This is because the ammeter measures current and current for two electrical components in series is the same.

8. What are the reciprocals of resistance and resistivity? What is its significance?

Ans: The reciprocals of resistance and resistivity are conductance and conductivity. They represent the material's ability to conduct the flow of current.

9. Is Ohm’s law valid for all types of devices? Why or why not?

Ans: No, Ohm’s law is valid only for certain devices which are known as Ohmic devices. This is because the variation of potential difference and current is not constant for all electrical devices.

10. Define electric current. What is its SI unit?

Ans: The flow of charge $(q)$ per unit time $(t)$ through a point is known as electric current. It can be represented as $\frac{q}{t}$. Its SI unit is Ampere.

Practical Based Questions

1. The current $I$ versus voltage $V$ plot of a certain electronic device is given below. The device is

1. A semiconductor

2. A conductor that obeys Ohm’s law

3. A superconductor

4. An insulator

Answer: (b)

2. In a circuit, a battery of terminal voltage $V$ is connected to a net resistance $R$. If $I$ current is drawn from the battery, then the power consumed by the battery is given by

1. $VI$

2. $\frac{V^2}{R}$

3. $I^2 R$

4. All of these

Answer: (d)

3. When an electric heater receives an electric current of $4A$ from the source, the potential difference across its ends is $60V$ . If the potential difference is increased to $127.5 V$ , then what will be the current received by the heater?

1. $24 \ A$

2. $10 \ A$

3. $8.5 \ A$

4. $12 \ A$

Answer: (c)

4. Ohm’s law is applicable to

1. Silicon carbide

2. Zener diode

3. Voltage regulator tubes

4. Copper

Answer: (d)

5. According to Ohm’s law, which of the following is constant?

1. $VQ$

2. $\frac{I}{V}$

3. $IT$

4. $\frac{V}{I}$

Answer: (d)

6. Ohm’s law can also be taken as a statement for

1. Conservation of energy

2. Conservation of electric charge

3. Conservation of angular momentum

4. Non-conservation of momentum of the flowing charge

Answer: (a)

7. The potential difference between two points of a wire carrying $2 \ A$ current is $0.1 \ V$. The resistance of the wire is

1. $0.05 \ \Omega$

2. $0.5 \ \Omega$

3. $5 \ \Omega$

4. $0.25 \ \Omega$

Answer: (a)

8. Volt per ampere is also called

1. Ohm-meter $(\Omega m)$

2. Joule

3. Ohm $(\Omega)$

4. Mho $(Ohm^{-1})$

Answer: (c)

9. In a laboratory, an experiment goes with resistance to show it follows Ohm’s law. Which of the following statement(s) is required for true results

1. Temperature remains constant

2. The graph between $V$ and $I$ is a straight line

3. $I \ = \ V \times R$

4. Both (a) and (b)

Answer: (d)

10. Which one of the following devices is non-Ohmic?

1. Conducting copper coil

2. Electric heating coil

3. Semiconductor diode

4. Rheostat

Answer: (c)

Summary

The opposition to the flow of electrons is resistance. Ohm's law explains the linear variation of a potential difference $V$ across the ends of a conductor, with current $I$ flowing through it. The constant defined here is resistance $R$, which depends on the material and dimensions of a conductor. Resistance of conductors is also dependent on temperature, and it increases with temperature. By Ohm’s law, one can also find the resistance by plotting a $V-I$ graph.