The document Theory & Procedure, Metre Bridge (Law of Combination of resistors) Class 12 Notes | EduRev is a part of the Class 12 Course Physics Class 12.

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**Our Objective:**

To verify the laws of resistances in series and parallel.

**The Theory:**

**Metre Bridge**

The metre bridge, consists of a one metre long wire of uniform cross sectional area, fixed on a wooden block. A scale is attached to the block. Two gaps are formed on it by using thick metal strips in order to make the Wheat stone’s bridge. The terminal B between the gaps is used to connect galvanometer and jockey.

The metre bridge is operates under Wheatstone’s principle. Here, four resistors P, Q, R, and S are connected to form the network ABCD.

In the balancing condition, there is no deflection on the galvanometer. Then,

A resistance wire is introduced in gap G_{1} and the resistance box is in gap G_{2}. One end of the galvanometer is connected to terminal D and its other end is connected to a jockey. As the jockey slides over the wire AC, it shows zero deflection at the balancing point (null point).

If the length AB is l, then the length BC is ( 100-l ).

Then, according to Wheatstone’s principle;

Now, the unknown resistance can be calculated as,

**Resistors in Series**

When two or more resistors are connected such a way that one end of one resistor is connected to the starting end of the other, then the circuit is called a Series Circuit.

When the two resistors X_{1} and X_{2} are connected in series in a circuit, the current I passing through each resistor is same.

Using Ohm’s Law, the potential difference V_{1} across X_{1} is:

Let Xs be the effective resistance of the two resistors in series, and V be the potential difference across the ends.

Thus, when a number of resistors are connected in series, the effective resistance is equal to the sum of the individual resistances. This is called the law of combination of resistances in series.

Adding resistors in series always increases the effective resistance.

**Resistors in Parallel**

If the starting ends of two resistors are joined to a point and the terminal ends of the two are combined and given connection to a source of electricity,those circuits are called **Parallel Circuit.**

When the two resistors X_{1} and X_{2} are connected in parallel in a circuit, the potential difference across X_{1 }and X_{2} are the same.

Then the current passing through the circuit is,

If there are ‘n’ number of resistors with different resistances connected in parallel, then we have,

That is, for a set of parallel resistors, the reciprocal of their equivalent resistance equals the sum of the reciprocals of their individual resistances. Thus, resistance decreases in parallel combination.

**Learning Outcomes:**

**Related Video: Metre Bridge (Law of Combination of resistors)**

- The student learns the following concepts:
- Resistance in a circuit.
- When two resistors are connected in series, its equivalent resistance increases.
- Law of combination of resistors connected in series.
- When two resistors are connected in parallel, its equivalent resistance decreases.
- Law of combination of resistors connected in parallel.

**Materials required:**

- Metre bridge (slide wire bridge)
- Battery (Leclanche cell)
- Galvanometer
- Resistance box (0.1 to 10 ohm)
- Jockey
- One way key
- Two resistance wires
- Screw gauge
- Metre scale
- A set square
- Connecting wires

**Procedure**:

- Make sure you first draw the circuit diagram and arrange the metre bridge apparatus.

- Connect the resistance wire whose resistance say X is to be determined in gap G
_{1}. Take care of that no part of the wire forms a loop and minimum portion of the wire is used for connection. - Connect a resistance box of low range in gap G
_{2}. - Make all other connections as in the circuit diagram.
- Take out some resistance (say 2Ω) from the resistance box.
- Insert the key in plug key to complete the battery circuit.
- Touch the jockey gently first at left and then at right end of the bridge wire. Note the deflections in the galvanometer. If the galvanometer shows deflections in opposite directions, the connections are correct. If the deflection is in one side only then there is some fault in the circuit, so the connections need to be checked.
- Allow the jockey to gently move or slide over the wire between A and C from left to right till galvanometer gives a null deflection (galvanometer reads the value 0)
- The point where the jockey is touching the wire is null point B.
- Place jockey in the middle of the wire (between 45cm to 55cm), choose an appropriate value of R from the resistance box such that the galvanometer shows null deflection.(Pointing 0)
- Note position of point B and measure the distance from the end where the resistance wire is connected to the point B. It is taken as the balancing length l1(AB)
- Also note the length CB (100-l).
- Interchange the resistances X and R. i.e, connect X in gap G
_{2}and R in gap G_{1} - Gently move jockey on the wire to attain null deflection in the galvanometer. (Shows zero in the galvanometer.)
- Note the reading balancing length l
_{2}(CB) and the length AB (100-l). - The mean balancing length is calculated. Repeat the experiment with different values of known resistance R.
- Using the formula X= , we can find out the unknown resistance.
- A mean value of the unknown resistance calculated will be considered as the value of unknown resistance.
- Connect two resistances X
_{1}and X_{2}in series and repeat the experiment keeping this combination in gap G1and vice versa. This gives the resistance of combination, X_{s}of X_{1}and X_{2}in series. - Connect two resistances X
_{1}and X_{2}in parallel and repeat the experiment keeping this combination in gap G1and vice versa.This gives the resistance of combination,Xp of X_{1 }and X_{2}in parallel.

**Simulator Procedure (as performed through the Online Labs):**

**Law of Resistances in Series**

- Your simulator will consist of a metre bridge kept on a table, battery, resistance box and wires on the side bar menu.
- You can calculate the resistance of a single wire or serially connected wire by selecting from the drop down menu, “Arrangement of Resistors”.
- If you selected, “Single”, then drag the battery and the resistance box shown on the side bar menu near to the metre bridge using your mouse.
- Drag one of the wires to the right gap of the metre bridge.
- Now the button, “Start experiment” will be enabled.
- Now you can select your desired resistance from the resistance box just by clicking on the box and then choosing the resistance from the pop-window, “Select Resistance”. Now close the pop-window.
- Click on the enabled button and "Insert Key”.
- Now you can move the jockey from one left end to right either by moving the jockey with your mouse or by moving the slider, “Jockey Position”.
- Simultaneously check the readings of the galvanometer, once the needle reaches the zero reading, stop moving the jockey and note down the length of the wire from the balanced position on the left side, let say “AB” which is l cm.
- Repeat the same by moving the jockey from the right end to the left and note down the length of the wire from the balanced position on the right side, let take it as “BC” which is 100-l cm.
- Repeat the same procedure with second wire and note down the lengths.
- For each wire take three readings and calculate its mean readings/resistance.
- Repeat the same procedures for the series connection.

**Related Test: Combination Of Resistors - Current Electricity, Class 12, Physics**

**Law of Resistances in Parallel**

- Your simulator will consist of a metre bridge kept on a table, battery, resistance box and wires on the side bar menu.
- You can calculate the resistance of a single wire or serially connected wire by selecting from the drop down menu, “Arrangement of Resistors”.
- If you selected, “Single”, then drag the battery and the resistance box shown on the side bar menu near to the metre bridge using your mouse.
- Drag one of the wires to the right gap of the metre bridge.
- Now the button, “Start experiment” will be enabled.
- Now you can select your desired resistance from the resistance box just by clicking on the box and then choosing the resistance from the pop-window, “Select Resistance”. Now close the pop-window.
- Click on the enabled button and "Insert Key”.
- Now you can move the jockey from one left end to right either by moving the jockey with your mouse or by moving the slider, “Jockey Position”.
- Simultaneously check the readings of the galvanometer, once the needle reaches the zero reading, stop moving the jockey and note down the length of the wire from the balanced position on the left side, let say “AB” which is l cm.
- Repeat the same by moving the jockey from the right end to the left and note down the length of the wire from the balanced position on the right side, let take it as “BC” which is (100-l) cm.
- Repeat the same procedure with second wire and note down the lengths.
- For each wire take three readings and calculate its mean readings/resistance.
- Repeat the same procedures for the parallel connection. (Here, you need to drag the wire twice to make a parallel connection).
**Observations:**

Unknown resistance | Trial No | Resistance from the resistance box (R ohm) | Balancing Length on the side of X | (100-l)cm | Unknown resistance
| Mean Resistance (ohm) | |||

X1 only | 1 | l _{1}(cm) | l _{2}(cm) | Mean l (cm) | X _{1} = | ||||

2 | |||||||||

3 | |||||||||

X2 only | 1 | X _{2 }= | |||||||

2 | |||||||||

3 | |||||||||

X1 and X2 in series | 1 | X _{s }= | |||||||

2 | |||||||||

3 | |||||||||

X1 and X2 in parallel | X _{p} = | ||||||||

**Calculation for verification of laws in series**

Experimental value of X_{s} = ........... ohm

Theoretical value of X_{s }= X_{1} + X_{2} = ........... ohm

Calculation for verification of laws in parallel

Experimental value of X_{p} = ........... ohm

Theoretical value of X_{p},

........... ohm

**Result**:

Experimental value of X_{s} = ohm

Theoritical value od X_{s }= ohm

Experimental value of X_{p} = ohm

Theoritical value of X_{p }= ohm

The experimental and the theoritical value of X_{s} and X_{p} are found to be the same. Hencew law of resistances in series and parallel is verified.

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