3.2 The Wheatstone bridge
Originally developed in the nineteenth century, a Wheatstone bridge provided an accurate way of measuring resistances without being able to measure current or voltage values, but only being able to detect the presence or absence of a current. A simple galvanometer, as illustrated in Figure 13, could show the absence of a current through the Wheatstone bridge in either direction. The long needle visible in the centre of the galvanometer would deflect to one side or the other if any current was detected, but show no deflection in the absence of a current.

Figure 14(a) shows a circuit made of four resistors forming a Wheatstone bridge. Its purpose here is to show whether there is any current flowing between and
. Figure 14(b) shows an equivalent way of drawing the circuit.

The bridge is said to be balanced (that is, no current flows through the bridge and the needle of the galvanometer shows no deflection) if the voltages and
are equal. It can be shown that the bridge is balanced if, and only if,
, as follows.
When then
. Then the Wheatstone bridge can be viewed as two voltage dividers,
and
on the left and
and
on the right. Applying the voltage divider equation gives
and
.
So

and

Multiplying out the brackets gives

which simplifies to

and

So, if were unknown,
,
and
could be chosen so that the needle of a galvanometer showed no deflection due to the current. Then

SAQ 4
Assume the Wheatstone bridge shown in Figure 14 is balanced. If ,
and
, what is the resistance of
?
Answer
By the formula given in the text,

OpenLearn - An introduction to electronics Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.