Understanding the Meter Bridge Setup
The meter bridge experiment uses a bridge wire to measure an unknown resistance. The bridge consists of a uniform wire of length 100 cm, and the unknown resistance is connected in one gap while a known resistance is connected in the other.

Key Concept: End Correction
- When measuring resistance, the assumption is that the bridge wire is perfectly uniform.
- However, due to the finite size of the contact points, the effective length of the wire is not exactly 100 cm, leading to a phenomenon known as end correction.

Deriving the End Correction Formula
1. **Basic Setup**:
- Let \( l \) be the length of the bridge wire used for the balance.
- Let \( R_1 \) and \( R_2 \) be the known and unknown resistances respectively.
2. **Balance Condition**:
- At balance, the ratio of resistances is given by:
\[
\frac{R_1}{R_2} = \frac{l}{100 - l}
\]
3. **Effective Length**:
- The actual length of the bridge wire (l) differs from the length measured due to end corrections (\( e \)):
\[
l' = l + e
\]
- Where \( e \) is the end correction.
4. **Modified Balance Condition**:
- Replacing \( l \) with \( l' \):
\[
\frac{R_1}{R_2} = \frac{l + e}{100 - (l + e)}
\]
- Rearranging allows solving for \( e \).
5. **Final Expression**:
- The expression can be simplified to find the end correction \( e \) based on the geometry of the setup and the resistances involved.

Conclusion
Understanding the end correction is essential for accurate measurements in a meter bridge setup. Incorporating this correction ensures that the theoretical assumptions align more closely with practical results.