3.Electrical Instrumentation lab manual for diploma electrical engineering 3rd sem as per GTU

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 0.01F.

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 ...

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2.Electrical Instrumentation lab manual for diploma electrical engineering 3rd sem as per GTU

PRACTICAL 2

AIM: - TEST THE LOW RESISTANCE USING KELVIN BRIDGE.

APPARATUS:-

• Regulated dc supply-1no
• Standard resistance coil-1no
• Kelvin’s double bridge kit.
• Digital multimeter-1no,
• Patch codes.

CIRCUIT DIAGRAM:-

CLICK ON GIVEN LINK

THEORY:-

               Kelvin’s bridge is a modification of whetstone’s bridge and always used in measurement of low resistance. It uses two sets of ratio arms and the four terminals resistances for the low resistance consider the ckt. As shown in fig. The first set of ratio P

And Q. The second set of ratio arms are p and q is used to connected to galvanometer to a Pt dat an Approx. potential between points m and n to eliminate the effects of connecting Lead of resistance r between the known std. resistance‘s’ and unknown resistance R .The ratio P/Q is made equal to p/q. under balanced condition there is no current flowing Through galvanometer which means voltage drop between a and b, Eab equal to the Voltage drop between a and c, Eamd.

Now

Ead=p/(p+q)

Eab=I[R+S+ ((p+q)r)/(p+q+r)]

Eamd=I[R+ p/p+q [(p+q) r/p+q+r]] 

For zero deflection->

Eac=Ead

[P/P+Q]I[R+S+ {(p+q) r/p+q+r}] =I[R+pr/p+q+r] —______________________(3)

Now, if

P/Q=p/q

Then equation… (3) Becomes

R=P/Q=S-_________ (4)

Equation (4) is the usual working equation. For the Kelvin’s Double Bridge .It indicates

The resistance of connecting lead r. It has no effect on measurement provided that the two Sets of ratio arms have equal ratios. Equation (3) is useful however as it shows the error that is introduced in case the ratios are not exactly equal. It indicates that it is desirable to keep as small as possible in order to minimize the error in case there is a diff. between

The ratio P/Q and p/q.

R=P/QS

OBSERVATION TABLE:-

Sr no.	P                         (Ratio Arm Resistor)	Q  (Ratio Arm Resistor)	S Standard Resistor	R Measured Value	R Actual

PROCEDURE:-

1) The circuit configuration on the panel is studied.

2) Supply is switched on and increased up to 5v.

3) The unknown resistance is connected as shown.

4) The value of P,Q was selected such that a. P/Q=p/q

5) S was adjusted for proper balance and balance value of s was balanced.

6) The value of known resistance was calculated.

PRECAUTIONS:-

1) Check all the connections before turning ON the power supply.

2) Do not exceed the value of 5v.

3) Note the readings accurately.

CONCLUSION:-

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1.Electrical Instrumentation lab manual for diploma electrical engineering 3rd sem as per GTU

PRACTICAL 1

AIM: - TEST THE MEDIUM RESISTANCE USING WHEATSTONE   BRIDGE.

v Specific Objective:-

        Student will be able to find out resistance of the above bridge.

v Apparatus:-

1.      Adtran’s trainer kit

2.      C.R.O

3.      Patch cords

4.      Digital multimeter

v Theory:-

    A very important device used in the measurement of medium resistances is the Wheatstone bridge. A whetstone bridge has been in use longer than almost any electrical measuring instrument. It is still an accurate and reliable instrument and is extensively used in industry. The Wheatstone bridge is an instrument for making comparison measurements and operates upon a null calibration principle. This means the indication is independent of calibration of the null indicating instrument or any of its characteristics. For this reason, very high degrees of accuracy can be achieved using Wheatstone bridge. Accuracy of 0.1% is quite common with a Wheatstone bridge as opposed to accuracies of 3% to 5% with an ordinary ohmmeter for measurement of medium resistances.

     Fig shows the basic circuit of a Wheatstone bridge/ it has four resistive arms, consisting of resistances P,Q,R, and S together with a source of emf (a  battery ) and a null detector, usually a galvanometer G or other sensitive current meter. The current through the galvanometer depends on the potential difference between points c and d. the bridge is said to be balanced when there is no current through the galvanometer or when the potential difference across the galvanometer is zero. This occurs when the voltage from point ‘b’ to point ‘a’ equals the voltage from point ‘d’ to point ‘b’; or, by referring to the other battery terminal, when the voltage from point ‘d’ to point ‘c’ equals the voltage from point ‘b’ to point ‘c’.

                 For bridge balance, we can write:

                                          I₁P = I₂R…………………………………………. (1)

 For the galvanometer current to be zero, the following conditions also exist:

                                          I₁ = I₃ =E/(P+Q)

                                          I₂ = I₄ =E/(R+S)…………………………… (3)

Where

        Combining Eqns. (1), (2), and (3) and simplifying, we obtain:

                                     P/(P+Q) =   R/(R+S)  …………………………. (4)

                                        QR = PS …………………………………………   (5)

Eqn.(5) is the well known expression for the balance of Wheatstone bridge. If three of the resistances are known, the fourth may be determined fro eqn. (5) and we obtain:

                               R = S P/Q…………………………... (6)

 Where R is the unknown resistance S is called the ‘standard arm’ of the bridge and P and Q are called the ‘ratio arm’.

v Procedure :-

1.      Connect the required supply and switch ON the unit. See that the supply LED glows.

2.      Observed the sine wave at the respective terminals.

3.      Now connects the C.R.O between the ground and the terminals marked ‘detector’.

4.      Connect the unknown resistance to the terminal marked S.

5.      Select one multiplier arm by connecting link.

6.      Vary P for minimum position.

7.      Similarly vary R  For minimum position.

8.      If the selection of the multiplier is correct the balance point can be observed on the C.R.O.

9.      Substitution the same in the formula and the value of S.

v Observation Table:-

SR.NO	P	Q	S (Multiplier arm)	R = S P/Q

v Calculation :-

v Conclusion :-

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