The Law of Combination (Series) of Resistances Using a Metre Bridge

A metre bridge is a device which works on the Wheatstone bridge idea. It is generally used to find the unknown resistance of a conductor. This device consists of a wire of one metre, which is why it is known as a “metre bridge”. The wire used to make the metre bridge is either nichrome, manganin or constantan. It is referred to as a slide wire bridge. This device is designed from a Wheatstone bridge. 

In this article, we will have a deep insight into the metre bridge formula and procedure to perform an experiment to verify the law of combination (series) of resistances using it.

Table of Contents:

• Aim

• Apparatus Required

• Theory

• Procedure

• Observations

• Result

• Precautions

• Lab Manual Questions

• Viva Questions

• Practical Based Questions

Aim

Metre Bridge Formula - To verify the laws of combination (series) of resistances using a metre bridge.

Apparatus Required

• Resistance box

• Leclanche cell and jockey

• Metre Bridge 

• Galvanometer and a key

• Sandpaper and connecting wires

• Two resistance wires or two resistance coils

• A set square

Theory

A metre bridge is based on the principle of Wheatstone bridge. The general arrangement of the Wheatstone bridge is shown in the figure below. It consists of four arms, DA, AB, BC and CD consisting of known and fixed resistances R1 and R3 and variable resistance R2 and unknown resistance Rx. The sensitive galvanometer is connected across terminals D and B. The battery is connected across other two terminals, A and C. 

Wheatstone Bridge

Wheatstone bridge is also used to measure capacitance and impedance and is based on the principle of null deflection. That means no current will flow through the middle arm of the circuit when the ratio of resistances in the two arms is equal. No current will flow through the galvanometer in the balanced condition. This situation arises when we get R1/R2 = R3/Rx, which is the balanced condition of the Wheatstone bridge. So, in this way, the unknown resistance Rx can be determined in terms of other known resistances of the Wheatstone bridge. 

A metre bridge consists of one metre-long constantan wire of uniform cross-sectional area mounted on a wooden board with a scale.

Circuit Diagram Of Metre Bridge

Two ends of the wire are attached to terminals A and C which is shown here in the above circuit diagram. In the metre bridge, thick metal strips bent at right angles are used to provide two gaps to connect resistors. The terminal B which is between the gaps is used to connect the galvanometer and we should connect the other end of the galvanometer to a Jockey J. 

Series Combination of Resistances:

We know that, when two resistors ${{r}_{1}}$ and ${{r}_{2}}$ are connected in series, the resistance of their combination ${{R}_{S}}$ is given by,

${{R}_{S}}={{r}_{1}}+{{r}_{2}}$

The resistance of an unknown resistance wire or a coil is expressed by, (from the above figure)

$r=\dfrac{\left( 100-l \right)}{l}R$

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

Procedure

• First of all, we need to mark the two resistance coils as ${{r}_{1}}$ and ${{r}_{2}}$.

• Now, connect the wire in the right gap between C and B, whose resistance is to be determined, and we should connect the resistance box $R$ in the left gap between A and B as shown in the circuit diagram of the metre bridge. The arrangement of the other apparatus should be as shown in the circuit diagram of the metre bridge.

• Carefully tighten all the plugs in the resistance box $R$ by pressing and rotating each plug to ensure that all the plugs make good electrical connections. Then, using sandpaper, clean the ends of connecting wires before making the connections.

• After that, we need to remove some plugs from the resistance box $R$ and plug the key K.

• Now, slide the jockey gently along the wire from left to right till the galvanometer gives zero deflection. The deflections in the galvanometer should be in opposite directions and if it is in one direction, then we can say that the circuit connections are not correct.

• Let D be the null point where the jockey is touching the wire and the movement of the jockey should be gentle from left to the right of the galvanometer and obtain a null point D on the metre bridge wire by sliding it gently between the ends A and C. 

• Note the value of resistance $R$ and lengths AD and DC and calculate the experimental value of the equivalent series resistance.

• Repeat this experiment for two more values of resistance $R$ and obtain the mean value of unknown resistance.

• Repeat the above steps by connecting ${{r}_{2}}$ and then by connecting resistances ${{r}_{1}}$ and ${{r}_{2}}$ in series in the right gap between C and B and record the observations as given in the table below. 

Observations

• The theoretically expected value of the series combination resistances is ${{R}_{S}}={{r}_{1}}+{{r}_{2}}$ 

• Here, we can obtain ${{r}_{1}}$ and ${{r}_{2}}$ from colour code on carbon resistors or are the given values in case of resistances made of wires of materials like nichrome, constantan etc.

Result

• We can conclude from the experiment that within limits of experimental error, theoretical and experimental values of ${{R}_{S}}$ are the same. Hence, we can say that we have verified a series combination of resistances using the metre bridge. So, the law of resistance in series is verified.

Precautions

• All the connections and plugs should be neat, clean and tight.

• The jockey should be moved gently over the metre bridge wire.

• Plug keys of the resistance box should be tight by rotating it in a clockwise direction, and null points should be in the central region of the wire.

Lab Manual Questions 

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

Ans: It alters the area of the cross-section of the wire, which in turn changes the resistance per unit length of the wire. So, we should not rub the jockey on the metre bridge’s wire. 

2. From which metal metre bridge’s wire is formed?

Ans: Nichrome, constantan and manganin are generally used to form metre bridge’s wire because they have very low temperature coefficient.

3. What is a galvanometer?

Ans: A galvanometer is an accurate and sensitive instrument which is used to measure and detect electric current.

4. When is Wheatstone Bridge said to be balanced?

Ans: The Wheatstone bridge is said to be balanced when no current flows through the galvanometer.

Viva Questions

1. What is Metre Bridge? 

Ans: Metre bridge is an instrument through which we can find the resistance of any given wire. It is a modified form of Wheatstone’s network.

2. On which principle does the metre bridge work?

Ans: Metre bridge works on the Wheatstone’s bridge principle.

3. What is the need of a combination of resistances?

Ans: The need of combination of resistances is to get the desired range of required resistance for the electrical circuit.

4. Which quantity remains the same in a series combination of resistors?

Ans: Current (I) remains the same in a series combination of resistors.

5. Why do we use a galvanometer in this experiment?

Ans: To find a balanced point or zero deflection point, we use the galvanometer in this experiment.

6. Which is the latest version of the metre bridge?

Ans: Carey Foster Bridge is the latest version of the metre bridge.

7. What type of galvanometer is generally used in a laboratory?

Ans: Pivoted Coil Weston type galvanometer is generally used in a laboratory. 

8. What is resistance?

Ans: It is a property of a conductor by virtue of which it resists the flow of current through it. Its SI unit is ohm.

9. What happens to the equivalent resistance when we connect three resistances in series combination?

Ans: The equivalent resistance increases when we connect three resistances in series combination.

10. Why do we use copper blades in the metre bridge?

Ans: We use copper blades in the metre bridge because the resistance of copper is negligible.

Practical Based Questions

1. Where can we obtain the balance point in the metre bridge?

1. At right end of the wire

2. At any point of the wire

3. At left end of the wire

4. At the mid point of the wire 

Ans: Option D - At the mid point of the wire 

2. _____ is independent of the radius of the wire.

1. The balance point of the metre bridge

2. The unbalanced point of the metre bridge

3. Fuse of the metre bridge

4. None of the above

Ans: Option A - The balance point of the metre bridge

3. _____ value of resistance can be found using the metre bridge.

1. Moderate 

2. High

3. Low

4. All of the above

Ans: Option A - Moderate 

4. Which instrument can be used to measure resistance?

1. Voltmeter

2. Voltameter

3. Ammeter

4. Ohmmeter

Ans: Option D - Ohmmeter 

5. The symbol for voltage is? 

1. W

2. VO

3. V

4. Amp

Ans: Option C - V

6. What happens if we connect two or more resistances in series combination?

1. The voltage through each resistance would be same

2. The current through each resistance would be same

3. Option A and B

4. None of the above

Ans: Option B - The current through each resistance would be same

7. Which of the following statements are correct?

1. The metre bridge is based on the principle of Wheatstone bridge

2. The metre bridge is used to find unknown resistance and it is also called a slide wire bridge

3. Option A and B

4. None of the above

Ans: Option C - Option A and B

8. When two resistances are connected in the series combination, then the effective resistance _____.

1. Increases

2. Decreases

3. Becomes half

4. Does not change

Ans: Option A - Increases

9. We should connect an ammeter in _____ across the cell.

1. Series

2. Triangular

3. Either series or triangular

4. Parallel

Ans: Option A - Series

10. What do we measure using a Wheatstone Bridge?

1. Radius of the bridge wire

2. Voltage

3. Power

4. Resistance

Ans: Option D - Resistance

Conclusion

From the above experiment, we can conclude that the difference of theoretical and experimental value in series combination is very small. So, the law of series combination of resistances is verified.