Wheatstone Bridge:

Construction, Principle,
Applications and Limitations
Wheatstone Bridge, a very important tool for measurement and
experiments, is used to measure the value of an unknown resistance in an
electrical circuit. Samuel Hunter Christie created the initial design of a
Wheatstone Bridge. In his design, the bridge had a diamond-shaped
arrangement with four resistors. Thus, he called it “Diamond Bridge”. He
used the bridge to compare the electromagnetic forces in different metals.
Based on the work of Samuel, in 1843, Charles Wheatstone designed the
Wheatstone Bridge that we work with today. The Wheatstone Bridge design
led to the development of the Meter Bridge, Wein Bridge, and the Carey
Foster Bridge.

What is Wheatstone Bridge?

A Wheatstone Bridge is basically an electrical circuit set up to compare
resistances or measure the unknown value of a resistor’s resistance by
creating a balance between the two legs of the bridge circuit. It is also
known as a ‘resistance bridge’. Wheatstone bridge uses the comparison
method to measure the value of unknown resistance.

The Wheatstone Bridge consists of four resistors put together in a diamond-

shaped circuit. Although initially developed to measure the value of
unknown resistance, it can be used to calibrate measuring instruments like
voltmeters, ammeters, etc., with the help of variable resistance and a
simple mathematical formula. The Wheatstone bridge circuit gives the quite
accurate value of measured resistance.

Wheatstone Bridge Construction

A Wheatstone bridge has four arms which consist of two known resistance,
one variable resistance and one unknown resistance, the value of which has
to be determined. The circuit includes an emf source and galvanometer. The
basic circuit of the Wheatstone bridge is shown in the figure below.
The bridge has four resistors   R1, R2, R3 and  R4. A source is connected across
one pair of diagonally opposite points ( A and  C in the figure).  AC is the battery
arm. A galvanometer   G (a device to detect currents) is connected
between  B and  D. This line, shown as  BD in the figure, is called the
galvanometer arm. The electromotive source is connected between
points  A and  C. The current that flows across the galvanometer is determined by
the potential difference applied across it.

What is Wheatstone Bridge Principle?

A Wheatstone bridge is based on the principle of null deflection, i.e. when
the ratio of resistances in the two arms is equal, no current flows will flow
through the middle arm of the circuit. A galvanometer is connected in the
middle arm, so when zero current passes through the galvanometer, then
the bridge is said to be in a balanced condition. Therefore, in the balanced
condition, the voltage difference between points   BB and  DD becomes zero,
i.e., at both points voltage level would be at the same potential. This
condition can be achieved by adjusting the known resistances   P,QP,Q and
the variable resistance  S.S. Although under normal conditions, the bridge
remains unbalanced, i.e. some current flows through the galvanometer.
Wheatstone Bridge Working
Consider the diagram of the Wheatstone bridge as shown below. It consists
of four resistance  P,Q,RP,Q,R and  SS with a battery of EMF  E.E. Two
keys  K1K1 and  K2K2 are connected across terminals A and C and B and D,
respectively. First, connect the key   K1K1 and then press the
key  K2.K2. Check if the galvanometer shows any deflection. If there is a
deflection, adjust the value of variable resistance till the galvanometer gives
a null deflection. When the galvanometer does not show any deflection,
then the Wheatstone bridge is said to be balanced.

Since the galvanometer does not show any deflection, thus, no current is
flowing through the galvanometer and terminals   BB and  DD are at the same
potential. In this condition,
PQ=RS.PQ=RS.
The arm containing resistors   PP and  QQ is sometimes referred to as the
ratio arm. To find the value of unknown resistance, the resistor is connected
in place of  S,S, and  RR’s (the variable resistor) resistance is varied
accordingly to achieve a null condition. Then, the value of unknown
resistance can be given as:
S=QPR
The arms  BDBD and  ACAC are called conjugate arms of the bridge. This is
because when the bridge is balanced, then interchanging the positions of
the galvanometer and the battery; there is no effect on the balance of the
bridge. The bridge is very reliable and gives an accurate result. The working
of the bridge is similar to the potentiometer. We employ the Wheatstone
bridge for determining the medium-range resistance. Thus, this method is
not suitable for the measurement of very low and very high resistance.
Sensitive ammeters are used to measure high resistance.

Wheatstone Bridge Derivation

When the Wheatstone bridge is balanced, no current flows through the
galvanometer i.e.  IG=0.IG=0. Thus, the current flowing across
arms  ABAB and  ACAC will be  I1I1 and the current through
arms  ADAD and  DCDC will be  I2.I2. According to Kirchhoff’s circuital law,
the voltage drop across a closed loop is zero. Thus, applying Kirchhoff’s
loop law across the loop  ABDA,ABDA, the sum of voltage drop along each
arm of the loop will be zero. The potential across each resistor is equal to
the product of its resistance and the current flowing through it, thus:
I1P–I2R=0I1P–I2R=0
I1I2=RPI1I2=RP……(i)
Similarly, applying Kirchhoff’s loop law across the loop   CBDC,CBDC, we
get:
I1Q–I2S=0I1Q–I2S=0
I1I2=SQI1I2=SQ….(ii)
From equations (i) and (ii), we get:
RP=SQRP=SQ
Or  PQ=RSPQ=RS
This is the condition for a balanced Wheatstone bridge.

Wheatstone Bridge Sensitivity

When we deal with measuring devices, sensitivity plays a major role in
determining their usefulness. A more sensitive device is considered better
and provides much more reliable results. When all the resistances are
equal, or their ratio is equal to   1,1, i.e. unity, such a Wheatstone bridge is
more sensitive. For any value of this ratio, the sensitivity of the bridge
decreases. This means that the bridge is the most accurate when the
resistances are almost comparable.
Wheatstone Bridge Applications
1. It is difficult to measure the resistance precisely, using ohm’s law. In
any such circuit, an ammeter and voltmeter are attached across the
unknown resistor to measure the current and voltage through it. But
 both these devices have their own limitations, leading to inaccurate
results. Thus, the Wheatstone bridge can be used in such a circuit to
measure precise results.

2. Materials like metals, semiconductors and insulators, all show

different behavior with the temperature variations. The changes in
their temperature can be measured by using thermistors in the bridge
circuit. A thermistor is a device whose resistance is temperature
reliant.
3. We can measure strain and pressure using a Wheatstone bridge.

4. By replacing the unknown resistance with a photoresistor, the

Wheatstone bridge can measure the variations in incident light.
Wheatstone Bridge Errors
Following are the errors which can occur while measuring a value using the
Wheatstone bridge.
1. The true value and the mentioned value of the resistance might be
different, and this difference can cause a measurement error.
2. There might be inaccuracies in measurement due to less sensitivity of the
galvanometer.
3. The self-heating of the bridge might alter its resistance and lead to an
error in calculation.
4. The generation of thermal reasons can lead to errors in the measurement
of low-value resistance.
5. Personal errors can occur when the person taking the reading is not
being careful.
We can avoid the errors mentioned above by using the best qualities
resistor and galvanometer. To minimize the error due to self-heating of
resistance, we should measure the resistance quickly. By connecting a
reversing switch between battery and bridge, thermal errors can be
reduced.

Limitations of Wheatstone Bridge

When the bridge is in an unbalanced state, it gives inaccurate readings. We
can use the Wheatstone bridge to calculate the value of resistance from a
few ohms to megaohms only. To measure any value lower or higher than
this, the circuit needs to be modified. By applying a suitable emf, the upper
range of the bridge can be increased, while by connecting lead at the
binding post, the lower range can be improved.

Summary
Wheatstone bridge is a device that uses the comparison method to measure
the value of minimum resistance. The value of this unknown resistance is
calculated by comparing it with a known resistance. A Wheatstone bridge
has four arms which consist of two known resistance, one variable
resistance and one unknown resistance, the value of which has to be
determined.

The circuit includes an emf source and galvanometer. A Wheatstone bridge

is based on the principle of null deflection, i.e. when the ratio of resistances
in the two arms is equal, no current flows will flow through the
galvanometer. This is the condition for a balanced Wheatstone bridge: PQ=RS