Question

With a circuit diagram, explain how a meter bridge can be used to determine unknown resistance of a given wire.

Hint:

A meter bridge uses the principle of the Wheatstone bridge to measure unknown resistance by balancing the bridge and using the ratio of resistances and lengths.

Answer 1

Step 1: Understanding the meter bridge.
A meter bridge is a device used to measure the unknown resistance of a wire using the principle of a Wheatstone bridge. It consists of a long, horizontal wire (usually made of constantan) mounted on a wooden or metallic base. The wire is stretched along a meter scale, and a jockey is used to make contact with the wire at various points.
Step 2: Wheatstone Bridge Setup.
The meter bridge consists of four resistors: 1. The wire of length \( 1 \, \text{m} \) which is uniform and has a known resistance per unit length. 2. A known resistance \( R_2 \) (the resistance of a known wire or resistor). 3. An unknown resistance \( R_x \), which we want to find. 4. A galvanometer to detect current flow.
The setup is as follows: \[ \begin{array}{c} \text{Known Resistance } R_2 \quad \parallel \quad \text{Wire (meter scale)} \quad \parallel \quad \text{Unknown Resistance } R_x
\hline \end{array} \] The jockey is moved along the bridge wire, and a null point is found where the galvanometer shows no deflection. At this point, the bridge is said to be "balanced." Step 3: Principle of operation.
When the meter bridge is balanced, the ratio of the resistances is equal to the ratio of the lengths of the bridge wire on either side of the jockey. This can be written as: \[ \frac{R_1}{R_2} = \frac{l_1}{l_2} \] where:
- \( R_1 \) is the known resistance, - \( R_2 \) is the unknown resistance, - \( l_1 \) and \( l_2 \) are the lengths of the bridge wire on either side of the jockey, such that \( l_1 + l_2 = 1 \, \text{m} \).
Step 4: Formula for calculating the unknown resistance.
By rearranging the formula above, we can calculate the unknown resistance: \[ R_x = R_2 \times \frac{l_2}{l_1} \] where \( l_1 \) and \( l_2 \) are measured when the bridge is balanced.
Step 5: Conclusion.
By using a meter bridge and applying the Wheatstone bridge principle, the unknown resistance can be determined by measuring the lengths at the null point and using the above formula.