Question

What is end error in a meter-bridge? How is it overcome? The resistance in the two arms of the meter-bridge are R = 5 Ω and S, respectively.

When the resistance S is shunted with an equal resistance, the new balance length found to be 1.5l₁, where l₁ is the initial balancing length. Calculate the value of S.

Answer 1

End error: The shifting of zero of the scale at different points as well as the stray resistance due to non-uniformity of metal wire gives rise to end error in meter bridge.

How to overcome end error? End error can be removed by repeating the experiment by interchanging unknown and known resistance and finally taking the mean value of resistance obtained in each experiment.

Given: The resistance in two arms of meter bridge are R = 5 Ω and 5 Ω.

According to Wheatstone bridge principle, we have the condition at balancing point as

After shunting the resistance S by equal resistance, new balance length is 1.5l₁. Shunting means connecting resistance in parallel. Thus, after shunting the new resistance, we get

and l₁ = 1.5l₁. Using Wheatstone bridge principle, we get

Using Eq. (1), we get

That is, 

Substituting the value of l₁ = 100/3 and R = 5 in Eq. (1), we get