Physics – To Verify The Laws Of Parallel Combination Of Resistances Using A Metre Bridge Experiment

Introduction

Verifying The Laws Of Parallel combination of resistances using a metre bridge is an experiment performed by high school students. It involves using a metre bridge to verify the law of parallel combinations.

The law of parallel combination of resistances states that “when two or more resistances are connected parallelly, the sum of the reciprocal of individual resistances is equal to reciprocal of equivalent resistances.

This law can be verified by the use of Ohm’s law. You can also use a meter bridge to verify this law experimentally. A meter bridge is also called a slide-wire bridge. It works on the principle of the Wheatstone bridge. It is used to calculate the unknown resistance of a conductor.

What is the law of parallel combination of resistances?

The law of parallel combination of resistance is a physics law that states that, “In case of a parallel combination of resistors, the sum of reciprocals of individual resistances is equal to the reciprocal of equivalent resistance”.

1/R = 1/r₁ + 1/r₂ + 1/r₃

Such that

R = equivalent resistance

r₁, r₂ and r₃ = resistances connected parallelly.

This law can be proved with the help of Kirchoff’s Law or Ohm’s law. One can also perform experiments on the meter bridge to prove this law. This experiment must be performed by students to understand the working of a meter bridge.

Verification through Ohm’s law

According to the Ohm’s Law, the total current in a circuit can be calculated by dividing the voltage by resistance.

I = V/R

One also knows that the total current in a circuit can be derived by adding all currents.

I = I₁ + I₂ + I₃

Since the voltage remains the same in all resistors in parallel combination, one can say,

V/R = V/r₁ + V/r₂ + V/r₃

1/R = 1/r₁ + 1/r₂ + 1/r₃

This represents that the equivalent resistance of three resistors in parallel combination is equal to the reciprocal of the sum of individual resistances. Thus, verifying the Law of the parallel combination of resistances.

What is a meter bridge?

A meter bridge is an experimental apparatus that works on the principle of the Wheatstone bridge. It is also called a slide-wire bridge and gets used for calculating unknown resistance in a conductor.

The Wheatstone bridge is a type of electric circuit. It helps in measuring unknown resistances by balancing the two legs of the circuit. It was created by Samuel Hunter Cristie in 1833 and further improved by Sir Charles Wheatstone in 1843.

A meter bridge is also similar to a Wheatstone bridge. It helps in the accurate measurement of resistances in a resistor. This device may be made of Manganin, constantan, or nichrome wires. Since these wires have low-temperature coefficients of resistance and high value of resistance, they are suitable.

One can also increase the sensitivity of a meter bridge. It is done by equating the resistance value of the four resistors. This makes the meter bridge a highly useful and powerful device.

Verify the Laws of Parallel Combination of Resistances Using a Metre Bridge Experiment

Now that one understands all the basics of the experiment. Let’s perform the experiment for verification of the law of parallel combination using a meter bridge.

Aim:

To verify the laws of the parallel combination of resistances using a meter bridge experiment.

Material Needed:

• 2 or more carbon or wire wound resistances
• Metre bridge
• Galvanometer
• Battery eliminator or cell
• Jockey
• Rheostat
• Plug key
• Resistance box
• Sandpaper
• Thick connecting wires

Theory:

Considering the two resistance r₁ and r₂, are connected in a parallel combination.

The equivalent of resistances in parallel series can be calculated by:

1/R = 1/r₁ + 1/r₂

R = r₁r₂/(r₁ + r₂)

Where

R = equivalent resistance

r1 and r₂ = resistances connected in parallel

Procedure:

1. Set up the circuit according to the standard circuit diagram.
2. Connect resistances r₁ and r₂ in parallel combination.
3. Ensure all the plugs in a resistance box are tight. Press and rotate each plug to assure good electric connections.
4. Clean the ends of connecting wires before connecting with the help of sandpaper.
5. Remove required plugs from the resistance box to get desired resistance value R.
6. Slide the jockey between A and C to get a null point D on the meter bridge.
7. Note down the value of length AD and DC and the resistance R.
8. Calculate the values of equivalent parallel resistance.
9. Repeat the experiment a few times to get four or more values of R.
10. Obtain the mean value of unknown resistance.

Precautions:

• Ensure all connections are tight, clear, and neat.
• Insert key only while taking observations.
• Be gentle when moving the jockey across the meter bridge.

Sources of Error:

• Loose connection of instrument screws.
• Thick connecting wires may be unavailable.

Result:

• The experimental value of R can be found.
• The theoretical value of R can be found.
• The experimental and theoretical values of R must be the same. Hence proving the law of parallel combination of resistances using a metre bridge experiment.

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