Basically electrostatic instruments are all
voltmeters. Fractically such instruments may be used for measurement of current
and power but both the types of measurements require measurement of voltage
across a known impedance. The main advantage of such instruments is the
measurement of high voltage in both a.c.
and d.c. circuit without any errors due
to eddy current losses and hysteresis.
1.1 Principle of operation
The operation of all electrostatic instruments
is based on the principle that there exists a force between the two plates with
opposite charge. This force can be obtained using the principle that the
mechanical work done is equal to the stored energy if there is a relative
motion of plates.
Consider two plates A and B where plate A is
fixed while B is movable. Two plates are oppositely charged and plate B is
restrained by a spring connected to
fixed point. Let the force of attraction between the two plates be F newton.
Let the capacitance between the two plates be C farad.
The energy stored E is the given by,
When applied voltage increases by dV, the
current flowing through capacitance also changed and it is given by,
The input energy is given by,
Also due to change in applied voltage by value
dV, the capacitance increases by Dc. Because plate B moves towards a fixed
plate A which decreases the distance of separation between two plates
increasing net capacitance.
Thus the new energy stored is given by,
The change in stored energy is given by,
Neglecting higher order terms of small
quantities such as dC and dV, we can write,
From the principle of the conversation of
energy, we can write input energy = increment in stored energy = increment in
stored energy + mechanical work done.
From above expression it is clear that the
force of attraction is directly proportional to the square of applied voltage
V.
The above theory can be extended to the
rotational motion, with the angular deflection θ in place of the linear displacement
x.
If the meter uses the spring control with
torsional spring constant K than,
Such an instrument can be used for a.c. and
d.c. measurements as the deflection is proportional to the square of the
voltage to be measured. It shows square law response hence the scale is nonunifom which is compressed at the lower end.