PRACTICAL 3
AIM: - TEST THE INDUCTANCE BY USING UNIVERSAL IMPEDANCE BRIDGE
OBJECTIVE: - To find the unknown inductance of a
coil or inductor using Anderson’s bridge. As a universal impedance bridge.
v APPARATUS:-
Sl. NO.
|
NAME
|
TYPE
|
RANGE
|
QTY.
|
1
|
Anderson’s bridge
circuit
|
1 no
|
||
2.
|
Head phones
|
1 no.
|
||
3.
|
Decade inductance box
|
1 no.
|
||
4.
|
DMM
|
DIGITAL
|
1 no.
|
|
5.
|
Patch cards
|
1set
|
||
6
|
RPS
|
230
|
1 no
|
|
7
|
Galvanometer
|
1 no
|
v CIRCUIT DIAGRAM:
CLICK ON THE LINK
v THEORY :
Anderson’s bridge is a modification of the Maxwell’s inductance capacitance bridge. In this method, the self-inductance is measured in terms of a standard capacitor. This method is applicable for precise measurement of self-inductance over a very wide range of values.
Figure shows the connections and the phasor diagram of the bridge for balanced conditions:
Let L1 = Self-inductance to be measure
R1 = resistance of self-inductor,
r1 = resistance connected in series with self-inductor,
r, R2, R3, R4 = known non-inductive resistances, and
C = fixed standard capacitor.
At balance, I1 = I3 and I2 = Ic + I4
Now I1R3 = Lc x Ic = I1jωCR3.
Writing the other balance equations
I1 (r1+R1+jωL1) = I2 R2 + Icr and Ic = (I2 – Ic) R4.
Substituting the value of Ic in the above equations, we have
I1(r1+R1+jωL1) = I2R2+I1jωC R3r
Or
I1(r+R1+jωL1-jωCR3r) = I2R2 …(i)
and
jωCR3 I1 = (I2 – IjωCR3)R4 or I1(jωCR3r + jωCR3R4 +R3) = I2R4… (ii)
From Eqns. (i) and (ii), we obtain
I1 (r1 + R1 + jωl1 – jωCR3r) = I1
Equating the real and the imaginary parts : R1 =
and L1 = C [r(R4 + R2) + R2R4]
An examination of balance equations reveals that to obtain easy convergence of balance, alternate adjustments of r1 and should be done as they appear in only one of the two balance equations.
v ADVANTAGES:
1.
In case adjustments are carried out by
manipulating control over r1 and r, they become independent of each
other. This is a marked superiority
over sliding balance conditions met with low Q coils when measuring axwell’s
bridge. A study of convergence conditions
would reveal that it is much easier to obtain balance in the case of Anderson’s
bridge than in Maxwell’s bridge for low Q-coils.
2. A fixed capacitor can be used instead of a
variable capacitor as in the case of Maxwell’s bridge.
3.
This bridge may be used for accurate determination of capacitance in terms of
inductance.
v DISADVANTAGES:
1. The Anderson’s bridge is more complex than
its prototype Maxwell’s bridge. The
Anderson’s bridge has more parts and is more complicated to set up and
manipulate. The balance equations are
not simple and in fact are much more tedious.
2. An additional junction point increases the
difficulty of shielding the bridge.
Considering
the above complications of the Anderson’s bridge, in all the cases where a
variable capacitor is permissible the simpler Maxwell’s bridge is used instead of
Anderson’s bridge.
v PROCEDURE :
1. Connections are made as per the circuit
diagram with an audio oscillator and head phones connected to proper terminals
of the Anderson’s bridge.
2. Connect the unknown inductor ‘L’ as shown in
the circuit diagram.
3. Switch on the supply and select a certain
value of ‘C’ say 0.01F.
4. Adjust R1and r1alternately till the head
phones give minimum or no sound.
5. Note down the values of S, M and C at this
balanced condition.
6. Repeat steps (4) and (5) for the same
inductance by selecting different value of C.
7. Repeat the above steps for different values
of unknown inductance.
8. Switch off the supply.
v NOTE :
1. The value of ‘C’ is so chosen that there is
sufficient adjustment available in the value of M.
2. When ‘C’ is small, ‘M’ will be large.
3. The bridge is useful for measuring small
values of inductor such as 50, 100, 150 and 200 mH.
Note
the value of unknown inductances
1.
10mH
2.
100mH
v OBSERVATION:-
S.NO
|
C(knowm capacitance)
|
r1
|
R1
|
R2
|
R3
|
R4
|
L1
|
v CALCULATION :
‘L’ value is calculated
by the given formula.
L1 = C R3/R4 [r1(R4+ R2) + R2R4]
R1 = R2R3/R4-r1
v CONCLUSION:-
FOR CIRCUIT DIAGRAM ...
PLEASE CLICK ON THE BELOW LINK...
