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

Metre Bridge - An Introduction

A metre bridge is a practical application of a Wheatstone bridge. It consists of a wire of one metre length and of uniform area of cross-section. Material used for making wire of metre bridge is constantan or manganin. We use constantan or manganin to make the wire of the metre bridge because they offer high resistance and low temperature coefficient of resistance. Metre bridge is most commonly used to calculate the resistance of a given resistor to determine the unknown resistance. 

Table of Contents

• Aim

• Apparatus Required

• Theory

• Procedure

• Observations

• Result

• Precautions

• Lab Manual Questions

• Viva Questions

• Practical Based Questions

Aim

To verify the law of combination (parallel) 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

Metre bridge is one of the forms of Wheatstone bridge. Wheatstone bridge is used to measure resistance, capacitance and impedance and is based on the principle of null deflection. The arrangement of a Wheatstone bridge is shown in the diagram given below. It is an arrangement of four resistances, P, Q, R and S in quadrilateral form to determine one unknown resistance of any four of them. That means, no current will flow through the middle arm of the circuit, when the ratio of resistances in the two arms is equal. The balanced condition arises when we get $\dfrac{P}{Q}=\dfrac{R}{S}$.

Wheatstone Bridge

A metre bridge consists of thick strips of copper of negligible resistance. There are two gaps between these three strips. A jockey is connected to B through a galvanometer G. Across the two ends of wire, a battery and a key are connected.

Circuit Diagram Of Metre Bridge

One end of the galvanometer is made to slide on the metre bridge wire. With this jockey, we search for a point on the bridge which corresponds to a null point. A null point is a point where the galvanometer shows no deflection and the bridge is balanced. When the bridge is balanced, the ratio of wire AB to the resistance of wire BC will be equal to the ratio of resistance R to the unknown resistance which is connected between the gap BC. Least error is obtained when the null point lies at the midpoint of the wire.

Parallel Combination of Resistances: 

When resistances are connected in parallel.

Parallel Combination Of Resistances

We know that, when three resistors ${{r}_{1}}$ , ${{r}_{2}}$ and ${{r}_{3}}$ are connected in parallel, the resistance ${{R}_{P}}$ of their combination is given by,

${{R}_{P}}=\dfrac {{r_1}{r_2}{r_3}}{{r_1}{r_2}+{r_2}{r_3}+{r_3}{r_1}}$

Procedure

• First of all, connect ${{r}_{1}}$ in the gap between B and C and tighten all plugs in the resistance box. Before making the connection, we should clean the ends of connections with sandpaper. Then connect the circuit as shown in the circuit diagram above.  

• Now, remove some plugs from the resistance box in order to get the suitable value of resistance R. 

• Get a null point D on the metre bridge by sliding the jockey between A and C ends. Then, we should note the length of AD and DC and value of resistance R.

• We need to evaluate the experimental value of the equivalent resistance of parallel combination.

• Now, perform this experiment two more times to obtain more values of resistance R. Then find out 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 parallel as shown in the above circuit diagram and record the observations as shown in the table given below. 

Observations

Verification of Parallel Combinations Theoretically and Experimentally.

1. Experimental value of $R_P$ = _____

2. Theoretical value of ${R_P}=\dfrac {{r_1}{r_2}}{{r_1}+{r_2}}$

3. Difference found (If any)=1.____
         =2.____

Result

• From this experiment, we can conclude that the theoretical and experimental value of ${{R}_{P}}$ is the same. Hence, we can say that we have verified a parallel combination of resistances using the metre bridge. So, the law of resistance in parallel is verified.

Precautions

• We should note down the readings without any parallax.

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

• We should insert the key only while taking observations. So, we can avoid heating of resistance, otherwise its resistance will increase. 

Lab Manual Questions 

1. State the law of combination of resistance in parallel combination.

Ans: It states that when we connect two or more resistances in parallel combination, the reciprocal of equivalent resistance is equal to the sum of the reciprocal of all the individual resistances. 

2. Which quantity remains the same in a parallel combination of resistors?

Ans: Voltage (V) remains the same in a parallel combination of resistors.

3. 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.

Viva Questions

1. When is Wheatstone bridge said to be balanced?

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

2. Which material should we use for a metre bridge wire?

Ans: We should use Constantan or Manganin for the metre bridge wire because their temperature coefficient of resistance is almost negligible.

3. In what way, household appliances be connected?

Ans: Household appliances must be connected in parallel.

4. How many common points are required when we connect two resistors in parallel combination?

Ans: We require minimum two common points when we connect two resistors in parallel combination.

5. Name the type of connection that we should use in our house wiring.

Ans: We should use a parallel connection of appliances in our house wiring. 

6. 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.

7. What happens to the equivalent resistance when we connect three resistances in parallel combination?

Ans: The equivalent resistance decreases when we connect three resistances in parallel combination. 

8. Can we use copper wire in the metre bridge? 

Ans: We can not use copper wire in the metre bridge because its temperature coefficient value is high and its specific resistance value is low. 

Practical Based Questions

1. Which instrument should we place at the centre of the Wheatstone bridge?

1. Inductor

2. Capacitor

3. Galvanometer 

4. Ammeter

Ans: Option C - Galvanometer 

2. Which of the following is true for the Wheatstone bridge?

1. We can use it to measure the internal resistance of the battery

2. We can use it to measure the electrical resistance

3. It is used to measure the intensity of magnetic field

4. It is used to measure the intensity of electric field

Ans: Option B - We can use it to measure the electrical resistance

3. In Wheatstone bridge, the instrument which we use as null detector is

1. Electroscope

2. Barometer

3. Spectrometer

4. Galvanometer 

Ans: Option D - Galvanometer

4. Which of the following statements are correct?

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

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

3. Option A and B

4. None of the above

Ans: Option C - Option A and B

5. Using a Wheatstone bridge, we can measure

1. Magnetic field

2. Radius of the bridge wire

3. Resistance

4. Electric field

Ans: Option C - Resistance

6. What happens if we connect two or more resistances in parallel 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 A - The voltage through each resistance would be same

7. The SI unit of resistance is 

1. Kelvin

2. Voltage

3. Ohm

4. Tesla

Ans: Option C - Ohm

8. The SI unit of current is

1. Ampere

2. Ohm

3. Tesla

4. Newton

Ans: Option A - Ampere

9. Which instrument can be used to measure resistance?

1. Refractometer

2. Voltmeter

3. Ohmmeter

4. Barometer

Ans: Option C - Ohmmeter

10. The symbol for voltage is 

1. T

2. Amp

3. Nm

4. V

Ans: Option D - V

Conclusion

From the above experiment, we can conclude that 

• The difference of theoretical and experimental value in parallel combinations is very small. So, the law of parallel combination of resistances is verified.

• To decrease the net resistance of the circuit, different resistors can be connected in parallel. 

• The potential difference across all resistors remains the same and the net resistance produced is lowest when resistors are connected in parallel.