4.4 Measurement of
capacitance and loss angle. (Dissipation factor)
4.4.1 Dissipation
factors (D)
A practical capacitor is represented as the series combination of small resistance and ideal capacitance.
From the vector diagram, it can be seen that the angle between voltage and current is slightly less than 900 . The angle ‘ δ ’ is called loss angle.
4.4.2 Desauty’s
Bridge
C1= Unknown capacitance
At balance condition,
4.4.3 Modified
desauty’s bridge
Advantages
r1 and c1 are independent of frequency.
They are independent of each other.
Source need not be pure sine wave.
4.4.4 Schering bridge
E1 = I1r1 − jI1X 4
C2 = C4= Standard capacitor (Internal resistance=0)
C4= Variable capacitance.
C1= Unknown capacitance.
r1= Unknown series equivalent resistance of the capacitor.
R3=R4= Known resistor.
Dissipation factor of capacitor,
Advantages
In this type of bridge, the value of capacitance can be measured accurately. It can measure capacitance value over a wide range.
It can measure dissipation factor accurately.
Disadvantages
It requires two capacitors.
Variable standard capacitor is costly.
4.5 Measurements of
frequency
24.5.1 Wein’s bridge
Wein’s bridge is popularly used for measurements of frequency of frequency. In this bridge, the value of all parameters are known. The source whose frequency has to measure is connected as shown in the figure.
NOTE
The above bridge can be used for measurements of capacitance. In such case, r1 and C1 are unknown and frequency is known. By equating real terms, we will get R1 and C1. Similarly by equating imaginary term, we will get another equation in terms of r1 and C1. It is only used for measurements of Audio frequency.
4.5.2 High Voltage
Schering Bridge
(1) The high voltage supply is obtained from a transformer usually at 50 HZ.
4.6 Wagner earthing
device:
Wagner earthing consists of ‘R’ and ‘C’ in series. The stray capacitance at node ‘B’ and ‘D’ are CB, CD respectively. These Stray capacitances produced error in the measurements of ‘L’ and ‘C’. These error will predominant at high frequency. The error due to this capacitance can be eliminated using wagner earthing arm.
Close the change over switch to the position (1) and obtained balanced. Now change the switch to position (2) and obtained balance. This process has to repeat until balance is achieved in both the position. In this condition the potential difference across each capacitor is zero. Current drawn by this is zero. Therefore they do not have any effect on the measurements.
What are the sources
of error in the bridge measurements?
Error due to stray capacitance and inductance.
Due to external field.
Leakage error: poor insulation between various parts of bridge can produced this error.
Eddy current error.
Frequency error.
Waveform error (due to harmonics)
Residual error: small inductance and small capacitance of the resistor produce this error.
Precaution
The load inductance is eliminated by twisting the connecting the connecting lead.
In the case of capacitive bridge, the various arm are electro statically screen to reduced the stray capacitance between various arm.
To avoid the problem of spike, an inter bridge transformer is used in between the source and bridge.
The stray capacitance between the ends of detector to the ground, cause difficulty in balancing as well as error in measurements. To avoid this problem, we use wagner earthing device.
4.7 Ballastic
galvanometer
This is a sophisticated instrument. This works on the principle of PMMC meter. The only difference is the type of suspension is used for this meter. Lamp and glass scale method is used to obtain the deflection. A small mirror is attached to the moving system. Phosphorous bronze wire is used for suspension.
When the D.C. voltage is applied to the terminals of moving coil, current flows through it. When a current carrying coil kept in the magnetic field, produced by permanent magnet, it experiences a force. The coil deflects and mirror deflects. The light spot on the glass scale also move. This deflection is proportional to the current through the coil.
4.8 Measurements of
flux and flux density (Method of reversal)
D.C. voltage is applied to the electromagnet through a variable resistance R1 and a reversing switch. The voltage applied to the toroid can be reversed by changing the switch from position 2 to position ‘1’. Let the switch be in position ‘2’ initially. A constant current flows through the toroid and a constant flux is established in the core of the magnet.
A search coil of few turns is provided on the toroid. The B.G. is connected to the search coil through a current limiting resistance. When it is required to measure the flux, the switch is changed from position ‘2’ to position ‘1’. Hence the flux reduced to zero and it starts increasing in the reverse direction. The flux goes from + φ to - φ , in time ‘t’ second. An emf is induced in the search coil, science the flux changes with time. This emf circulates a current through R2 and B.G. The meter deflects. The switch is normally closed. It is opened when it is required to take the reading.
4.8.1 Plotting the BH
curve
The curve drawn with the current on the X-axis and the flux on the Y-axis, is called magnetization characteristics. The shape of B-H curve is similar to shape of magnetization characteristics. The residual magnetism present in the specimen can be removed as follows.
Close the switch ‘S2’ to protect the galvanometer, from high current. Change the switch S1 from position ‘1’ to ‘2’ and vice versa for several times.
To start with the resistance ‘R1’ is kept at maximum resistance position. For a particular value of current, the deflection of B.G. is noted. This process is repeated for various value of current. For each deflection flux can be calculated.( B = φ/A )
Magnetic field intensity value for various current can be calculated.().The B-H curve can be plotted by using the value of ‘B’ and ‘H’.
4.8.2 Measurements of
iron loss:
Let
RP= pressure coil resistance
RS = resistance of coil S1
E= voltage reading= Voltage induced in S2
I= current in the pressure coil
VP= Voltage applied to wattmeter pressure coil.
W= reading of wattmeter corresponding voltage V
W1= reading of wattmeter corresponding voltage E
In the case of no load test the reading of wattmeter is approximately equal to iron loss. Iron loss depends on the emf induced in the winding. Science emf is directly proportional to flux. The voltage applied to the pressure coil is V. The corresponding of wattmeter is ‘W’. The iron loss corresponding E is E=WE/V. The reading of the wattmeter includes the losses in the pressure coil and copper loss of the winding S1. These loses have to be subtracted to get the actual iron loss.
4.9 Galvanometers
D-Arsonval Galvanometer
Vibration Galvanometer
Ballistic C
4.9.1 D-arsonval
galvanometer (d.c. galvanometer)
Galvanometer is a special type of ammeter used for measuring A or mA. This is a sophisticated instrument. This works on the principle of PMMC meter. The only difference is the type of suspension used for this meter. It uses a sophisticated suspension called taut suspension, so that moving system has negligible weight.
Lamp and glass scale method is used to obtain the deflection. A small mirror is attached to the moving system. Phosphors bronze is used for suspension.
When D.C. voltage is applied to the terminal of moving coil, current flows through it. When current carrying coil is kept in the magnetic field produced by P.M. , it experiences a force. The light spot on the glass scale also move. This deflection is proportional to the current through the coil. This instrument can be used only with D.C. like PMMC meter.
4.9.2 Vibration
Galvanometer (A.C. Galvanometer )
The construction of this galvanometer is similar to the PMMC instrument except for the moving system. The moving coil is suspended using two ivory bridge pieces. The tension of the system can be varied by rotating the screw provided at the top suspension. The natural frequency can be varied by varying the tension wire of the screw or varying the distance between ivory bridge piece.
When A.C. current is passed through coil an alternating torque or vibration is produced. This vibration is maximum if the natural frequency of moving system coincide with supply frequency. Vibration is maximum, science resonance takes place. When the coil is vibrating , the mirror oscillates and the dot moves back and front. This appears as a line on the glass scale. Vibration galvanometer is used for null deflection of a dot appears on the scale. If the bridge is unbalanced, a line appears on the scale.
Example 2.2-In a low-
Voltage Schering bridge designed for the measurement of permittivity, the
branch ‘ab’ consists of two electrodes between which the specimen under test
may be inserted, arm ‘bc’ is a non-reactive resistor R3 in
parallel with a standard capacitor C3, arm CD is a
non-reactive resistor R4 in parallel with a
standard capacitor C4, arm ‘da’ is a
standard air capacitor of capacitance C2. Without the specimen
between the electrode, balance is obtained with following values , C3=C4=120 pF, C2=150 pF, R3=R4=5000Ω.With the specimen inserted, these values
become C3=200 pF,C4=1000
pF,C2=900 pF and R3=R4=5000Ω. In such test w=5000 rad/sec. Find the
relative permittivity of the specimen?
Example 4.3- A
specimen of iron stamping weighting 10 kg and having a area of 16.8 cm2 is tested by an episten square. Each of the
two winding S1 and S2 have 515 turns. A.C. voltage of 50 HZ
frequency is given to the primary. The current in the primary is 0.35 A. A
voltmeter connected to S2 indicates 250 V.
Resistance of S1 and S2 each equal to 40 Ω. Resistance of pressure
coil is 80 kΩ. Calculate maximum flux density in the specimen and iron loss/kg
if the wattmeter indicates 80 watt?
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