Balaji Engineering College
Measurement of inductance by using AC bridge
Prepared by:Lakhnotra Kanji(131090109021)
2.Operation of AC Bridge
• A.C. Bridges are those circuits which are used to
measured the unknown resistances, capacitance
,inductance, frequency and mutual inductance.
• Inductance and capacitance can also be measured
by four-arm bridge.
• In this case the alternating current source is
employed by a vibration galvanometer.
Operation of AC Bridge:
When the specific circuit conditions
apply, the detector current becomes
zero, which is known as null or
Since zero current, it means that
there is no voltage difference
across the detector, Figure .
Voltage at point b and c are equal.
I 1 Z1 I 2 Z 2
The same thing at point d.
I1 Z 3 I 2 Z 4
From two above equation yield
general bridge equation;
Figure Equivalent of Balance
(nulled) AC Bridge.
Figure : (a) and (b) are Simple AC Bridge Circuit.
• In the Maxwell’s bridge measure an unknown
inductance then becomes known in terms of
the capacitance. As shown in fig.
• It is used to measure unknown inductances
with capacitance standard.
Because the phase shifts of inductors and
capacitors are exactly opposite each other, a
capacitive impedance can balance out an
inductive impedance if they are located in
opposite legs of a bridge.
Lx R2 R3 C1
The impedance of the arm can be written as,
1 / Rc jC1
Z 2 R2
Substitute in the balance equation,
Set real and imaginary part,
Z 3 R3
Z 4 R x jX LX
( R x jX LX ) R2 R3
1 / R1 jC1
R x jX LX
L x R2 R3 C1
jR2 R3 C1
• It is also a modification of the Maxwell’s
Bridge and is particularly useful if the
phase angle of the inductive impedance is
• It used as resistance in series with
capacitor. For large angel phase angle R1
have a very low value, this circuit is used
for measuring high Q.
• The Hay circuit is used for
measuring high-Q .
• Hay bridge for inductance
• Impedance triangles illustrate
inductive and capacitive phase
Z x Rx j Lx
1 j R3C3
Z 2 R2
2 R1R2 R3C32
1 2 R32C32
1 2 R32C32
Quality factor , Q Lx
• In the Anderson Bridge the unknown
inductance is measured in terms of a
known capacitance and resistance.
• this method is capable of precise
measurements of inductance over a wide
range of values from a few micro-henrys
to several henrys and is the best bridge
Measuring high Q
Equation for Owen’s bridge
The owen’s bridge is used for measurement of inductance
such that the inductance is expressed in term of
There no frequency components in L1 and R1
Balance condition is obtained much easily, because of
R2 and C2 are in same arm.