Electrostatic Instrument

ELECTROSTATIC INSTRUMENT

This instrument is used for both AC and DC measurement. This instrument has high resistance, so draws less current from the circuit and the force generated will be small. This instrument is best suited for voltage measurement. Voltage ranges from 100V to 20KV.

Principle:-

This instrument uses Electrostatic principle for producing deflection.

It consist of two plates one is fixed and the another one is movable voltage is applied between fixed and movable plate. Due to the accumulation of changes on the two plates, a force is generated, this force may be attractive or repulsive in nature. This cause the movable plate to be in motion. Motion may be linear or rotary based on the structure of the plate.

Quadrant Electrometer:

It is a type of Electrostatic instrument.

It consist of two fixed Quadrants and the Quadrants are arranged in a manner to form a hollow circular box with opening at the centre, movable needle flaced inside the hollow region and it is suspended with a wire. voltage to be measured is applied between the quadrand and the needle.

Wire is made up to phosphor bronze or silver Quartz. Quadrant electrometer may be used in two type of connection.

1. Heterostatic connection:

In this a battery is included in the circuit.

2. Idiostatic connection:

Torque equation:

When the voltage is being increased a capacitive current flows.

i = dq/dt = d(cv)/dt = c dv/dt + v dc/dt

multiply by vdt on both sides we get the input energy,

vidt = vc dv/dt . dt + v² dc/dt .dt

vidt = vc dv + v² dc ……….(1)

Energy stored = ½ cv²

Where 'c' is the capacitance between the two plates.

'v' is the voltage to be measured.

Change in stored energy = [ ½ (c + dc) (v + dv)²] - [ ½ cv²]

= [ ½ (c + dc) (v² + dv² + 2vdv) ] = ½ cv²

= ½ cv² + ½ cdv² + ½ c(2vdv) + ½ v² dc + ½ dcdv² + ½ dc(2vdv) – ½ cv²

Neglect are the higher order terms as they smaller quantities,

= ½ v² dc + cvdv ………..(2)

By the principle of conservation of energy,

input electrical energy = change in stored energy + mechanical work done

Equation (1) = Equation (2) + T_d dƟ

cvdv + v² dc = ½ v²dc + cvdv + T_d . dƟ

T_d . dƟ = v²dc - ½ v²dc

= ½ v²dc

T_d = ½ v² dc/dƟ

controlling torque is given by the spring

T_c = kᎾ

For final steady state deflection, T_c = T_d

kᎾ = ½ v² dc/dƟ

Ꮎ = ½ v²/k dc/dƟ

This instrument exhibits a square law response so it has non uniform scale.

Extension of meter range:

Range of Electrostatic instrument is extended by two methods.

1. Resistance potential divider:

The voltage to be measured (V) is connected to the resistance 'R' The electrostatic instrument whose range is to be extended is connected to a portion of the resistor.

multiplication factor, m = R/r

2. Capacitor multiplier

Here C₁, C₂, ……. C_n-1, C_n and C_p are set of series multiplier capacitors. Electrostatic instrument is connected across any one of these multiplying capacitors.

The equivalent capacitance,

1/C_series = 1/c₁ + 1/c₂ + ……. + 1/c_n-1 + 1/c_n

and C_v = C_p+ C_m

multiplication factor, m = V/V_m = 1+ (c_p + c_m)/C_s

Advantages:

1. Used for both AC and DC.

2. Deflecting torque is irrespective of polarity

3. Used for high voltage measurement.

4. Low power consumption.

Disadvantages:

1. Operating force is small

2. Non uniform scale.

3. High cost

4. Large size