Electrical and Electronic measurements & instrumentation
10EE35
Theory
AC bridges are often used to measure the value of unknown impedance (self/mutual inductance
of inductors or capacitance of capacitors accurately). A large number of AC bridges are available
and Anderson's Bridge is an AC bridge used to measure self inductance of the coil. It is a
modification of Wheatstones Bridge. It enables us to measure the inductance of a coil using
capacitor and resistors and does not require repeated balancing of the bridge. The connections
are shown in Fig: 1.
The bridge is balanced by a steady current
by replacing the headphone H by moving
coil galvanometer and A.C source by a
battery. This is done by adjusting the
variable resistance, r. After a steady balance
has been obtained, inductive balance is
obtained by using the A.C source and
headphone.
The condition for balance is that the
potentials at the terminals D and E are same. Then the current flowing through branch AB is
I1, through branch AE and EB is I2. The current flowing through branches AD and DC is I3,
while that through branch BC is I1+I2. No current flows through branch DE.
Circuit Details
Consider the mesh ABCDA
(1)
This shows that potential drop along ABC is equal to that along ADC.
Electrical and Electronic measurements & instrumentation
10EE35
Consider the mesh ABEA, there is no e.m.f.
(2)
Consider the mesh AEDA,
(3)
i.e.
potential
difference
From
from
A
to
E
is
equal
(3)
to
that
we
Now substitute the value of I3 from (1) in (4)
(5)
Dividing (5) by (2)
(6)
Multiply and divide by R in the L.H.S of (6) and rearrange,
(7)
(8)
Equation (8) represents the condition for balancing of the bridge.
A
to
D.
get,
(4)
Equating real parts on both sides of (7)
from
Electrical and Electronic measurements & instrumentation
10EE35
Equating imaginary parts on both sides of (7)
(9)
Substituting :
From (8) and (9) gives us
(10)
At this condition of balancing there is minimum sound in the headphone.
Further we can make P=Q
(11)
The inductive reactance can be calculated by
(11)
Notes:
1. Since the impedances of the arms should be of the same order of magnitude, the approximate
value of L should be determined by some other method. Then satisfying the
condition,
2. Sometimes it may be impossible to obtain the balance by varying r and S. Then the formula
for L with a value of RQ which satisfies formula for S may require negative value of r. If the
product CRq is greater than L, then variable resistance r will be a negative quantity. It will,
therefore, not possible to obtain a balace point under such conditions.Hence it is desirable to
know the value of L approximately so that CRQ is less than L. A balance is then obtained with a
positive value of r. The value of P and R should be then be adjusted so that r is a positive
quantity and a balance can be obtained by varying the value of r.
To obtain balance point a cathode ray oscilloscope can be used in place of heat phone.
Electrical and Electronic measurements & instrumentation
10EE35
Advantages
1. Fixed capacitor is used in terms of variable capacitor.
2. The bridge is used for accurate determination of inductance in millimeter range.
Disadvantages:
1. Bridge is more complex
2. Difficult to attain balancing condition.