Electrostatic Voltmeters

Electrostatic Voltmeters

Electrostatic Voltmeters

Electrostatic instruments such as Electrostatic Voltmeters are almost always used as voltmeters and that too more as a laboratory rather than as industrial instruments. The underlying principle of their operation is the force of attraction between electric charges on neighboring plates between which a potential difference is maintained. This force gives rise to a deflecting torque. Unless the potential difference is sufficiently large, the force is small. Hence, such instruments are used for the measurement of very high voltages. 

There are two general types of such instruments :
(i) The attracted disc type – used upto 500 kV.

(ii) The quadrant type-used upto 20 kV.

 

Electrostatic Voltmeters
Figure A

Attracted-disc Type Voltmeter


As shown in Figure A, it consists of two-discs or plates C and D mounted parallel to each other. Plate D is fixed and is earthed while C suspended by a coach spring, the support for which carries a micrometer head for adjustment. Plate C is connected to the positive end of the supply voltage. When a p.d. (whether direct or alternating) is applied between the two plates, then C is attracted towards D but may be returned to its original position by the micrometer head. The movement of this head can be made to indicate the force F with which C is pulled downwards.

For this purpose, the instrument can be calibrated by placing known weights in turn on C and observing the movement of micrometer head necessary to bring C back to its original position. Alternatively, this movement of plate C is balanced by a control device which actuates a pointer attached to it that sweeps over a calibrated scale.

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There is a guard ring G surrounding the plate C and separated from it by a small air-gap. The ring is connected electrically to plate C and helps to make the field uniform between the two plates. 

The effective area of plate C, in that case, becomes equal to its actual area plus half the area of the airgap.

Theory

In Figure B are shown two parallel plates separated by a distance of x meters. Suppose the lower plate is fixed and carries a charge of − Q coulomb whereas the upper plate is movable and carries a charge of + Q coulomb.

Electrostatic Voltmeters
Figure B

Let the mutual force of attraction between the two plates be F newtons. Suppose the upper plates is moved apart by a distance dx. Then mechanical work done during this movement is F × dx joule. Since charge on the plate is constant, no electrical energy can move into the system from outside. This work is done at the case of the energy stored in the parallel-plate capacitor formed by the two plates.

Before movement, let the capacitance of the capacitor be
C farad. Then,

If the capacitance changes to (C + dC) because of the movement of plate, then

http://engg.mcqsduniya.in/wp-content/uploads/2021/03/Electrostatic-Voltmeters-4.jpg

Hence, we find that force is directly proportional to the square of the voltage to be measured. 

The negative sign merely shows that it is a force of attraction.

Quadrant Type Voltmeters

The working principle and basic construction of such instruments can be understood from Figure C. A light aluminium vane C is mounted on a spindle S and is situated partially within a hollow metal quadrant B. Alternatively, the vane be suspended in the quadrant. When the vane and the quadrant are oppositely charged by the voltage under measurement, the vane is further attracted inwards into the quadrant thereby causing the spindle and hence the pointer to rotate. The amount of rotation and hence the deflecting torque is found proportional to V2. The deflecting torque in the case of arrangement shown in Figure C is very small unless V is extremely large.

Electrostatic Voltmeters
Figure C

The force on the vane may be increased by using a larger number of quadrants and a double-ended vane. In Figure D are shown four fixed metallic double quadrants arranged so as to form a circular box with short air-gaps between the quadrants in which is suspended or pivoted as aluminium vane.


Opposite quadrants AA and BB are joined together and each pair is connected to on terminal of the a.c. or d.c. supply and at the same time, one pair is connected to the moving vane M. Under these conditions [Figure D] the moving vane is recalled by quadrants AA and attracted by quadrants BB.


Hence, a deflecting torque is produced which is proportional to (p.d.)2. Therefore, such voltmeters have an uneven scale. Controlling torque is produced by torsion of the suspension spring or by the spring (used in pivoted type voltmeters). Damping is by a disc or vane immersed in oil in the case of suspended type or by air friction in the case of pivoted type instruments.

Electrostatic Voltmeters
Figure D

Theory


With reference to Figure C, suppose the quadrant and vane are connected across a source of V volts and let the resulting deflection be θ. If C is a capacitance between the quadrant and vane in the deflected position, then the charge on the instrument will be CV coulomb. Suppose that the voltage is charged from V to (V + dV), then as a result, let θ, C and Q charge to (θ + dθ), (C + dC) and (Q + dQ) respectively. Then, the energy stored in the electrostatic field is increased by

If T is the value of controlling torque corresponding to a deflection of θ, then the additional energy stored in the control will be T × dθ joule.

Total increase in stored energy = http://engg.mcqsduniya.in/wp-content/uploads/2021/03/Electrostatic-Voltmeters-8.jpg

It is seen that during this charge, the source supplies a change dQ at potential V. Hence, the value of energy supplied is

= V × dQ = V × d (CV) = V2 × dC + CV. dV

Since the energy supplied by the source must be equal to the extra energy stored in the field and the control

http://engg.mcqsduniya.in/wp-content/uploads/2021/03/Electrostatic-Voltmeters-9.jpg

The torque is found to be proportional to the square of the voltage to be measured whether that voltage is alternating or direct. However, in alternating circuits the scale will read r.m.s. values.

Read article – Parallel- Plate Capacitor

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