Verify The Laws of Combination (Series) of Resistances using a Metre Bridge

Table of Contents

Aim/Aim of Experiment

To verify the Laws of Combination (Series) of Resistances using a Metre bridge.

Apparatus/Materials Required

A Meter bridge
A Leclanche cell (Battery Emulator)
A Galvanometer
A Resistance Box
A Jockey
Two Resistance wires
A Set square
Sand Paper
Connecting wires.

Theory

(i) The resistance (r) of resistance wire or coil is given by r = (100−l)/L×R,

Where R is the resistance from the resistance box in the left gap, and L is the length of the Meter bridge wire from zero ends up to the balance point.

(ii) When two resistors r1 and r2 are connected in series, their combined resistance is given by R_s = r₁ + r₂.

Diagram

Law of combination series of resistances using Meter bridge

Procedure

Mark the two resistance coils as r₁ and r₂.
To find the value of r₁ and r₂, follow the same steps as Experiment 2. (if r₁ and r₂ unknown).
Connect the two coils r₁ and r₂ in series as shown in figure in the right gap of Meter bridge and find the resistance of this combination, Take at least three sets of observations.
Record your observations as follows.

Observations

Value of r₁:

Resistance of R.B. (ohm)	Balance L (cm)	(100-l) (cm)	[(100-l)*R]/l	Mean r₁
0.5	24	76	1.583
1	38	62	1.631	1.616
2	55	45	1.636

Value of r₂:

Resistance of R.B. (ohm)	Balance L (cm)	(100-l) (cm)	[(100-l)*R]/l	Mean r₂
0.5	33	67	1.015
1	50	50	1	1.015
2	66	34	1.030

Value of r_s:

Resistance of R.B. (ohm)	Balance L (cm)	(100-l) (cm)	[(100-l)*R]/l	Mean r_s
0.5	16	84	2.625
1	28	72	2.571	2.615
2	43	57	2.651

Calculations

Calculations for verification of laws r₁ and r₂ in series:

The Experimental value of R_s = 2.615 ohm.
The Theoretical value of R_s = r₁+r₂ = 1.616+1.015 = 2.631 ohm.
Experimental Error (Difference if any) = [(2.615-2.631)/2.615]×100 = 0.6%.

Result

Within limits of Experimental Error, Theoretical and Experimental values of R_s are the same. Hence, the law of resistance in series is verified.

Precautions

The Connection should be neat, clean and tight.
All the plugs in the resistance box should be tight.
Move the jockey gently over the bridge wire and don’t rub it.
Thick copper wires should be used for the connections after removing the insulations near their ends by rubbing with sand paper.
A low resistance rheostat should be used.
The key should be inserted only while taking observations to avoid heating of resistance (otherwise its resistance will increase).

Sources of Error

Resistance box, Instrument screw and other plugs may be loose.
Unavailable thickness connecting wires.
Used high resistance rheostat in connection.

Viva Voice Questions with Answers

1. What is a Metre bridge?

Answer: A Metre bridge also called a slide wire bridge, is an instrument that works on the principle Wheatstone bridge. A Meter bridge is used in finding the unknown resistance of a conductor as that of in a Wheatstone bridge.

2. How do you find the equivalent resistance of the series combination of resistance?

Answer: In series combination, the same current passes through each resistor in the chain and the total resistance Rs is given by the equation R_s = R₁+R₂+R₃+ ……..R_n.

3. How does resistance change in series combination?

Answer: Resistance increases in series combination.

4. Explain increase of resistance in series combination.

Answer: In series combination, the effective length of resistor increases. As R∝ l, resistance increases in series combination.

5. Why the jockey should not be pressed too hard on the wire when sliding over it?

Answer: Sliding the jockey with a hard press, will scratch the wire and make its thickness non uniform. Then the resistance per unit length of the wire will not remain constant because resistance depend upon area of cross-section.

6. What are end resistances?

Answer: The resistances of thick copper strips which keep the two ends of the wire pressed, are called end resistances.

7. What are the advantages of a Meter or Wheatstone bridge method of measuring resistance over other methods?

Answer: (i) It is a null method, hence the result does not get affected from extra resistances. (ii) It is easier to detect a small change in deflection than to read a deflection directly.

8. What do you mean by sensitiveness of a Meter or Wheatstone bridge?

Answer: A Meter/Wheatstone bridge is said to be sensitive if it produces more deflection in the Galvanometer for a small change of resistance in resistance arm.

9. When is a Meter or Wheatstone’s bridge said to be balanced?

Answer: A Meter or Wheatstone’s bridge is said to be balanced, when no current flows through the galvanometer and it gives zero deflection.

10. What is the condition for a Wheatstone’s bridge to become balanced?

Answer: In a balanced Meter/Wheatstone bridge, we have P/Q=R/S.

Class 12 Physics Practicals:

To Verify The Laws of Combination (Series) of Resistances Using A Metre Bridge