Electrostatic voltmeters are based on the fact that an electric force (attraction or repulsion) exists between charged plates or objects.
An electrostatic voltmeter is essentially an air condenser ; one plate is fixed while the other, which is coupled to the pointer, is free to rotate on jewelled bearings.
Electrostatic Voltmeter Working Principle
When p.d. to be measured is applied across the plates, the electric force between the plates gives rise to a deflecting torque. Under the action of deflecting torque, the movable plate moves and causes the deflection of the pointer to indicate the voltage being measured.
Such instruments can be used to measure direct as well as alternating voltages.
Types of Electrostatic Voltmeters
There are three types of electrostatic voltmeters viz. :
- Attracted disc type — usual range from 500 V to 500 kV
- Quadrant type — usual range from 250 V to 10 kV
- Multicellular type — usual range from 30 V in 300 V
Two things are worth noting about electrostatic voltmeters. First, the deflecting torque is very small for low voltages. For this reason, they are not very sensitive to measure small voltages.
Secondly, the instrument is only available for the measurement of p.d., that is to say as voltmeter. It cannot be used as an ammeter because when it is used as an ammeter, there will be a few millivolts voltage across the instrument. This extremely small p.d. is unsufficent to produce any deflecting torque.
Attracted Disc Type Voltmeter
Fig. 1 shows the simplified diagram of an attracted disc electrostatic voltmeter. It consists of two mushroom-shaped plates A and B, each mounted on insulated pedestal.
The plate B is fixed while the plate A (negative, for direct voltage) has a movable central portion – the attracted disc. The movable plate A is attached to a horizontal rod which is suspended by two phosphor bronze strips.
When p.d. to be measured is applied across the plates, the plate A moves towards the fixed plate B and actuates the pointer via a pulley or link mechanism. The control force is provided by gravity and damping force by air dash pot.
If the plates are too close together or if the applied voltage is too high, a spark discharge may occur. In order to prevent such a possibility, a ballast resistor is included in the circuit. The function of this resistor is to limit the current if any sparking-over occurs.
If the applied voltage reverses in polarity, there is a simultaneous change in the sign of charge on the plates so that the direction of deflecting force remains unchanged. Hence such instruments can be used for both d.c. and a.c. measurements.
Theory: The force of attraction F between the charged plates is given by ;
x = distance between the plates
C = capacitance between the plates
V = applied voltage
Since x is always samall, dC/dx is practically constanct.
Quadrant Type Electrostatic Voltmeter
Fig. 2 shows the simplified diagram of a quadrant type electrostatic voltmeter. It consists of a light aluminium vane A suspended by a phosphor-bronze string mid-way between two inter-connected quadrant shaped brass plates BB. One terminal is joined to fixed plates BB (positive for direct voltage) and the other to the movable plate A (negative for direct voltage).
Working: When the instrument is connected in the circuit to measure the p.d., an electric force exists between the plates. Consequently, the movable vane A moves in between the fixed plates and causes the deflection of the pointer. The pointer comes to rest at a position where deflecting torque is equal to the controlling torque.
Since the force of attraction between the movable plate A and the fixed plates BB is directly proportional to (p.d.)2, the instrument can be used to measure either direct or alternating voltages. When used in an a.c. circuit, it reads the r.m.s. values.
More robust but less accurate voltmeters are made by pivoting the moving system. Due to pivot friction, the pivoted voltmeters are less accurate than the suspension type. For this reason, low voltage electrostatic voltmeters are always of suspension type. In pivoted voltmeters, the —controlling torque is provided by a spiral spring.
The major drawback of quadrant type voltmeter is that deflecting torque is very small for low voltages. Because it also depends upon the capacitance between plates. In a quadrant voltmeter, the capacitance cannot be increased since the number of vanes is limited by space consideration. Therefore, such an instrument cannot measure accurately voltages below 250 V.
This difficulty has been overcome in a multicellular electrostatic voltmeter which can read as low as 30 volts.
Theory: The capacitance C between the plates depends upon deflection θ i.e., upon the position of the movable plate (or vane)A.
Suppose that at any instant, the applied alternating voltage is v. Electrostatic energy at that instant = Cv2/2
Since the capacitance between the plates depends upon deflection θ, the instantaneous deflecting torque T’d is given by ;
Where V = r.m.s. value of alternating voltage.
This equation equally applies to direct voltages. If dC/dθ were constant, then,
Td = I2
Hence the instrument has non-uniform scale. The non-linearity in the scale can be corrected by shaping the movable vane A in such a way as to increase dC/dθ for small deflections and to make the scale nearly uniform for larger ones.
Multicellular Electrostatic Voltmeter
Fig. 3 shows the constructional details of a multicellular voltmeter. It is essentially a quadrant type voltmeter with the difference that it has ten moving vanes instead of one and eleven fixed plates forming “cells” in and out of which the vanes move.
The moving vanes are fixed to a vertical spindle and suspended by a phosphor-bronze wire so that the vanes are free to move, each between a pair of fixed plates.
At the lower end of the spindle, an aluminium disc hangs horizontally in an oil bath and provides damping torque due to fluid friction. The controlling torque is provided by the torsion of the suspension wire as the moving system rotates.
The upper end of the suspension wire is attached through a coach spring S to a torsion head H. The torsion head is provided with a tangent screw for zero adjustment. The function of the coach spring is to prevent the suspension wire from breaking when accidentally jerked. If the moving vanes are jerked downward, then the coach spring yields sufficiently to allow the safety sleeve E to come into contact with the guide stop G before the suspension wire is over strained.
The scale is horizontal if the pointer is straight but the indications can be given on a vertical scale by bending the pointer at right angles. The working principle of multicellular voltmeter is exactly similar to the quadrant type.
By using a number of inter-leaved stationary and moving plates, we are able to increase the capacitance and hence the deflecting torque. Consequently. the multicellular voltmeter is much more sensitive than the quadrant type and can accurately measure low voltages.
Advantages Electrostatic Voltmeters
- They can be used for both d.c. and a.c. measurements.
- With direct voltage, the instrument draws only the initial charging current and with alternating voltages, the alternating current drawn is extremely small. So they draw negligible power from the mains. Therefore, such voltmeters do not alter the condition of the circuit to which they are connected.
- They are free from hysteresis and eddy current losses as no iron is used in their construction.
- Their readings are independent of waveform and frequency.
- They are unaffected by stray magnetic fields, although electrostatic fields may cause considerable errors.
Disadvantages Electrostatic Voltmeters
- The operating force is very small for low voltages so that they are particularly suitable for the measurement of high voltages.
- Since the operating force is generally small, errors due to friction are difficult to avoid.
- They are expensive, large in size and are not robust in construction.
- Their scale is non-uniform ; being crowded in the beginning of the scale.
Applications Electrostatic Voltmeters
- They are used for the measurement of very high direct voltages at which a permanent magnet moving coil instrument and the multiplier would be unsuitable.
- They are used to measure direct low voltages when it is necessary to preserve an open circuit.
- They are used to measure very high alternating voltages when the use of a transformer must be avoided.
Range Extension of Electrostatic Voltmeters
The range of electrostatic voltmeters can be increased by the use of multipliers. Two types of multipliers are employed for this purpose viz.
- Resistance potential divider – for ranges upto 40 kV
- Capacitance potential divider – for ranges upto 1000 kV
The first method can be used for both direct and alternating voltages whereas the second method is suitable only for alternating voltages.
Resistance potential divider: This divider consists of a high resistance with tappings taken off at intermediate points. The voltage V to be measured is applied across the whole of the potential divider and the electrostatic voltmeter connected across part of it (resistance r in this case) as shown in Fig. 4.
Since the voltmeter practically carries no current the p.d. v across it is the same fraction of the applied voltage V as the resistance across it (i.e. r) is of the whole resistance (i.e. R) i.e.,
Multiplying factor = V/v = R/r
Thus if the voltmeter is connected across 1/5 of the whole resistance (i.e. R/r = 5), then voltage V to be measured is 5 times the reading of the voltmeter. The advantage of this method is that there is no shunting effect of the voltmeter. The drawback is that there is power loss in the resistance divider.
Capacitance potential divider: In this method, a single capacitor of capacitance C is connected in series with the voltmeter and the whole circuit is connected across the voltage V to be measured as shown in Fig. 5.
Let v volts be the reading of the voltmeter. Since the voltage across a capacitor is inversely proportional to its capacitance.
By using capacitors of different capacities, different voltage ranges can be obtained. This method has the advantage that the circuit consumes no power. However, the drawback is that capacitance current taken is greatly increased.
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