# Metre wire bridge

## A practical arrangement of the Wheatstone bridge

In this version the two ratio arms of the
bridge are the two sections of a metre wire as shown in Figure 1. The circuit is shown in
Figure 1(a) and a practical arrangement in Figure 1(b).

A standard resistance S is
used and hence the value of the unknown resistance R can be found.

For this
bridge the balance condition (no current in the galvanometer) is given by the equation:

Balance condition: R = [L_{1}/L_{2}]S

## Accuracy of a metre wire bridge

Measurement of resistance with a metre wire bridge Let the unknown
resistor be R, the standard resistor be S and the two lengths of wire at the balance point be
L

_{1} and L

_{2} .

Therefore the fractional error in R is given
by:

DR/R =

DS/ S +

DL

_{1}/L

_{1} +

DL

_{2}/L

_{2}Therefore the greatest
accuracy is obtained when L

_{1} = L

_{2} for a given value of

DL. The balance point must be in the centre of the
wire.