Question

With the help of a circuit diagram describe the method to find the value of an unknown resistance using meter bridge arrangement.

Answer 1

Construction:

The circuit diagram for a meter bridge experiment is shown in the attached figure. It consists of a resistance coil 1 m long with a labelled meter scale in parallel to a known emf source of voltage $\epsilon$ and key $K$. The resistance coil is connected in parallel to a series combination of the resistance $X$ (device under test) whose value is to be found and a known resistance $Y$. $X$ and $Y$ are connected to each other and the circuit by a very low resistance material behaving as wires and the section in between $X$ and $Y$ is connected to a galvanometer. The other end of galvanometer is connected to the resistance of meter scale through an adjustable jockey.

Principle of working:

Meter bridge is based on the principle of wheatstone bridge and characteristics of linear resistance.

By principle of wheatstone bridge, null deflection in galvanometer is obtained only when $X:Y=R_1:R_2$.

Also, resistance is proportional to the length of the resistance coil.

Hence, at null point:

$X:Y=l_1:100-l_1$

Procedure:

1. Connect the circuit diagram properly.

2. Close the key $K$ so that the current flows in the coil.

3. Observe the deflection of the coil and adjust the jockey so that the deflection is reduced to zero.

4. Note down the values of $l_1$ & $l_2$.

5. Repeat steps 2 to 4 two more times.

6. Open the key.

Calculations:

From the values recorded above, find $X$ using the formula,

$X=Y\left(\frac{l_1}{100-l_1}\right)$ for all three measurements and find the average.