# What is end error in a meter bridge? How is it overcome? The resistances in the two arms of the meter bridge are $R=5\Omega$ and $S$ respectively. when the resistance $S$ is hunted with an equal resistance the new balance length found to be $1.5 \; l_{1}$, where $l_{1}$ is the initial balancing length. Calculate the value of $S.$

In the meter bridge, the zero of the ruler doesn't align with the starting end of the wire. This causes a type of zero error known as end error.

By using known values of $P$ and $Q$, we can determine the end error.

Theoretically, we can calculate the distance from $A$ at which the free end of the galvanometer be connected to get zero deflection.

Experimentally, we can also read the distance on the ruler.

On Substarcting the theoretical value from the reading will give us the zero error.

For meter bridge, applying whetstones bridge principle

$\frac{R}{S}=\frac{l_{1}}{100-l_{1}}$

We know that,

$\frac{R\Omega }{S}=\frac{l_{1}}{100-l_{1}}$ _____(1)

After putting an equal resistance in parallel with S, we have,

$\frac{2R}{S}=\frac{1.5\; l_{1}}{100-1.5\; l_{1}}$        ________(2)

On dividing equation (1) and (2)

We get

$\frac{1}{2}=\frac{100-1.5l_{1}}{1.5(100-\; l_{1})}$

Implies

$l_1=\frac{50}{1.5}$

On substituting the value of $l_1\ and \ R$ in equation (1)

We get

$S=10\Omega$

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