To Determine Resistance Per cm of A Given Wire By Plotting A Graph For V & I

Table of Contents

Aim/Aim of Experiment

To determine Resistance (R) per cm of a given wire by plotting a Graph for Potential difference (V) versus Current (I).

Apparatus/Material Required

A wire of unknown Resistance (Wire)
A Battery (Battery Eliminator)
A Voltmeter (0-3) Volt
An Ammeter (0-3) Ampere
A Rheostat
A Meter scale
One way Plug key
Connecting wires
A piece of Sand paper

Theory

According to the Ohm’s law, the electric current (I) flowing through a conductor is directly proportional to the Potential difference (V) across its ends, provided the physical state/conditions (pressure, temperature and dimensions) of the conductor remains unchanged or the same.

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

I∝V or V∝I

hence V = RI

or V/I = R (Main Formula)

Where R is the constant of proportionality and is termed as the Electrical resistance of the conductor. Resistance (R) depends on the Nature of material, Temperature & Dimensions of the conductor. In S.I. units, the potential difference V is measured in volt (V) and the current I in Ampere (A), The resistance R is measured in ohm.

Note: The relationship between the resistance of a material, its length and area of the cross-section is given by the formula:

R=ρlA,

Where ρ is the specific resistance or resistivity and it is a characteristic of the material of the given wire.

(i) To establish the current-voltage relationship, it is to be shown that the ratio V/I remains constant for a given resistance, Therefore a graph between the potential difference (V) and the electric current (I) must be a straight line.

(ii) The constant ratio gives unknown value of resistance, (V/I = R).

Circuit Diagram

to determine resistance per cm of a given wire By plotting a graph for potential difference (v) versus current (i) — Circuit diagram to determine resistance per cm of a given (unknown) wire.

Procedure

Clean the ends of the connecting wire with the help of sandpaper to remove any insulating coating on them.
Connect the Resistance, Rheostat, Battery, key, Voltmeter and Ammeter as shown in the figure.
Arrange the apparatus in the same manner as given in the arrangement or circuit diagram.
Make sure that the pointers in the Voltmeter and Ammeter coincide with the zero mark on the measuring scale. If not, adjust the pointer to coincide with the zero mark by adjusting the screw provided at the base using a screwdriver.
Make neat, clean and tight connections according to the circuit diagram. While making connections ensure that +ve marked terminals of Voltmeter and Ammeter are joined towards the +ve terminal of the battery.
Determine the Range and Least count of Voltmeter and Ammeter and also note the zero error if any.
Insert the key K and slide the rheostat to the end where the current flow is minimum. Ensure see that Voltmeter and Ammeter are working properly.
Adjust the sliding contact of the rheostat such that a measurable current passed through the resistance coil or the resistance wire.
Note down the value of Potential difference (V) from Voltmeter and Current (I) from Ammeter.
Shift the rheostat contact slightly so that both Ammeter and Voltmeter show full division readings and not in fraction.
Record the readings of the Voltmeter and Ammeter.
Take at least five sets of independent observations.
Now finally Cut the resistance wire at the points where it leaves the terminal, stretch it and find its length by the Meter scale.
Record your observations.

Observations

Length:
- Length of the Resistance wire l = 50 cm.
Range:
- Range of the given Ammeter = 0.3A.
- Range of the given Voltmeter= 0-3V.
Least Count:
- Least count of Ammeter = 0.05.
- Least count of Voltmeter = 0.05.
Zero Error:
- Zero error of Ammeter = nil.
- Zero error of Voltmeter = nil.
Zero Correction:
- Zero Correction for the given Ammeter = 0A.
- Zero Correction for the given Voltmeter = 0V.

Observations Table

Table for Ammeter and Voltmeter Readings:

Serial No. of Obs.	Ammeter Reading I (A) Observed	Voltmeter Reading V (V) Observed	V/I=R (ohm)
1.	0.10	0.75	7.5
2.	0.20	1.50	7.5
3.	0.30	2.25	7.5
4.	0.40	3.00	7.5

So, mean Value of Resistance R = 7.5 ohms.

Calculations

1. Find ratio of V and I for each set of observations.

2. Plot a graph between potential difference (V) and current (I), taking V along X-axis and I along Y-axis. After ploting the graph it’s comes to be a straight line as shown below.

From graph, the resistance can be calculated.

In ∆ABC tanø = AB/CB = ∆I/∆V,

or cotø = ∆V/∆I

but R = ∆V/∆I

Then, R = cotø

Therefore R = (3.00-0.75)/(0.40-0.10)

So, R = 7.5 ohm.

3. Constant ratio V/I gives resistance of the wire.

4. Resistance of the wire per centimetre (cm):

R = 7.5/50 ohm/cm (Ωcm^-1),

Therefore R = 0.15 Ωcm^-1.

Result

The Resistance of the given wire = 7.5 Ω (ohm).
The Resistance per cm of the wire = 0.15 Ωcm^-1 (ohm/cm).
Ohm’s law verified as the graph between Potential difference (V) and Current (I) is a straight line.

Precautions

The Connection should be neat, clean and tight.
Voltmeter and Ameter should be of proper range.
A law resistance of Rheostat must be used.
The key should be insert only while taking readings or observations to avoid heating of resistance (otherwise its resistance will increase).
Thick copper wires should be used for the connections after removing the insulations near their ends by rubbing with Sand paper.

Viva Voice Questions with Answers

Question 1: State Ohm’s Law.

Answer: Ohm’s law states that the electric current (I) flowing through a conductor is directly proportional to the potential difference (Voltage) V across its ends (provided that the physical conditions – temperature, pressure and dimensions of the conductor remain same).

Question 2: Give mathematical form of Ohm’s law.

Answer: Mathematical form of Ohm’s law is, V = RI, where V is the Potential difference, I is the Current and R is the constant of proportionality which is known as Resistance.

Question 3: Define resistance.

Answer: The constant ratio of potential difference V across the ends of a conductor to the current I flowing through it, is called resistance of the conductor. It is represented by the symbol R, R = V/I.

Question 4: How can be resistance measured?

Answer: Resistance can be measured by (i) Ohm’s law (ii) Metre bridge (iii) Multimeter.

Question 5: Define the unit of resistance.

Answer: The S.I. unit of resistance is Ohm (Ω) or volt per ampere. One ohm is the resistance of a conductor carrying current one ampere when unit p.d. is maintained across its ends, 1 ohm = 1V/1A.

Question 6: What is the cause of resistance?

Answer: Collisions of drifting electrons with the atoms.

Question 7: Which are the factors on which the resistance of a conductor depends on?

Answer: The resistance of a conductor depends on the following factors:

Resistivity
Length
Temperature
Cross-sectional area.

Question 8: What are Ohmic and non-ohmic resistances?

Answer: Resistances which obey Ohm’s law, are called ohmic resistances e.g., metals like Cu, Al, Ag etc. at low temperature. Resistances which do not obey Ohm’s law are called non-ohmic resistances e.g. diodes and transistors.

Question 9: What is ohm? Define it.

Answer: Ohm is the S.I. unit of resistance. One ohm is the resistance offered by a conductor when one ampere current is flowing through it, when one volt potential difference is maintained across its ends.

Question 10: What is a rheostat?

Answer: A rheostat is a variable resistance that is used to control the current.

Question 11: What is the shape of a Potential difference (V) vs Current (I) graph for a linear resistor?

Answer: The shape of the Potential difference V versus Current I graph for a linear resistor is a Straight line.

Question 12: What is the reciprocal of resistivity called?

Answer: The reciprocal of resistivity is called Conductivity.

Class 12 Physics Practicals:

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