Indicating Instruments Analog Instruments
Analog instruments are classified in one way as
a) Indicating b) Recording c) Integrating Instruments. Essential Requirements of an Instrument:
For satisfactory operation of any indicating instrument, following systems must be present in an instrument.
1. Deflecting system producing deflecting toque 2. Controlling system producing controlling torque 3. Damping system producing damping torque.
The deflecting system uses one of the following effects produced by current or voltage, to produce deflecting torque.
1. Magnetic Effect: When a current carrying conductor is placed in uniform magnetic field, it experiences a force which causes it to move. This effect is mostly used in many instruments like moving iron attraction and repulsion type, permanent magnet moving coil instruments etc.
2. Thermal Effect: The current to be measured is passed through a small element which heats it to cause rise in temperature which is converted to an e.m.f. by a thermocouple attached to it. When two dissimilar metals are connected end to end, to form a closed loop and the two junctions formed are maintained at different temperatures, then e.m.f. is induced which causes the flow of current through the closed circuit which is called a thermocouple.
3. Electrostatic Effect: When two plates are charged, there is a force exerted between them, which moves one of the plates. This effect is used in electrostatic instruments which are normally voltmeters.
4. Induction Effect: When a non-magnetic conducting disc is placed in a magnetic field produced by electromagnets which are excited by alternating currents, an e.m.f. is induced in it.
If a closed path is provided, there is a flow of current in the disc. The interaction between induced currents and the alternating magnetic fields exerts a force on the disc which causes to move it. This interaction is called an induction effect. This principle is mainly used in energymeters.
current, then an e.m.f. is produced between two edges of conductor. The magnitude of this e.m.f. depends on flux density of magnetic field, current passing through the conducing bar and hall effect co-efficient which is constant for a given semiconductor. This effect is mainly used in flux-meters.
Controlling System
It produces a force equal and opposite to the deflecting force in order to make the deflection of pointer at a definite magnitude.
Damping System
The quickness with which the moving system settles to the final steady position depends on relative damping.
Three types of damping exists 1. Critically damped 2. Under damped 3. Over damped
The following methods are used to produce damping torque. 1. Air friction damping
2. Fluid friction damping 3. Eddy current damping.
Under damped Over damped Critically damped Time Steady final position Deflection 0
Measurement of Voltage and Current Analog Ammeter and Voltmeters
The Instruments used for measurement of voltage and current can be classified as: a) Moving coil instruments
(i) Permanent magnet type (ii) dynamometer type b) Moving iron instruments c) Electrostatic Instruments d) Rectifier instruments e) Induction instruments f) Thermal instruments
(i) Hot - wire type (ii) Thermocouple type a) Moving Coil Instruments
(i) Permanent Magnet Type: It works on the principle of magnetic effect Torque equation:
The deflecting torque is given by = NBAI
Where – deflecting torque in N – m B – Flux density in air gap ⁄ . N – Numbers of turns of the coil A – effective coil area ) – length; b – breadth of the coil I – current in the moving coil, amperes
The controlling torque is provided by springs and is proportional to angular deflection of the pointer
θ
Where = controlling torque
K = spring constant, ⁄ or ⁄ θ = Angular deflection.
For the final steady state position,
G = NBA
Thus we get a linear relation between current and deflection angle.
Damping used in this type of instrument is eddy current damping. (ii) Dynamometer Type
Dynamometer instrument uses the current under measurement to produce the magnetic field.
Deflecting Torque Torque equation: T =
Where instantaneous value of current in fixed coils; A = Instantaneous value of current in moving coil; A M = Mutual inductance between fixed and moving coil; H Operation with D.C
Operation with A.C I = ( )
= ( )
T = time period for one complete cycle. Electrodynamometer Ammeters
θ =
Range: upto 100 mA.
Electrodynamometer Voltmeter
Moving Iron Instruments
Moving iron instruments depend for their indication upon the movement of a piece of soft iron in the field of a coil produced by the current to be measured.
Td = (1/2)I2(
). Where I is the current through the coil and L is the inductance.
Linearization of Scale: Compensation towards frequency errors can be done by connecting a capacitor across a part of series resistance in MI voltmeter, C = 0.41 (L/R2)
Electrostatic Instruments
For linear motion: F = (1/2) V2 ( )
For angular motion: Td = (1/2) V2 ( )
Rectifier Instruments
Half wave Rectifier type Instruments
Full wave rectifier type instruments:
Shunts and Multipliers
Shunts and multipliers are the resistance connected in shunt or series with ammeter and voltmeters to enhance their measuring capacity.
Shunt with ammeter I =
Instrument constant, m = I =
Multiplier with Voltmeter
m = R =
Shunt for a.c. instruments
Multiplication factor = Instrument V I of shunt V I Load R
Multipliers for Moving – Iron Instruments
voltage multiplying factor (m) = √
√
Measurement of Resistance Measurement of Low Resistance
Kelvin's Double Bridge is used for the measurement of low resistance as shown in fig
R =
* +
Measurement of Medium Resistance
Two wires are required to represent a medium resistance: Q P R S E p d q b a m n c r L R (Multiplier)
(R, L) resistance and inductance of the instrument
This can be measured by: a) Ammeter voltmeter method b) Wheatstone bridge method c) Ohm meter
a) Voltmeter - Ammeter Method From fig
Measured value of resistance,
Where R is the true value of the resistance. Error= Ra % Error = (Ra/R)
This method is suitable for measurement of high resistance, among the range.
Ammeter - Voltmeter Method % error =
This method is suitable for measurement of low resistance among the range.
The resistance where both the methods give same error is obtained by equating the two errors. R = √
b) Wheat stone Bridge
=
Sensitivity of the galvanometer, Where = deflection of the galvanometer
e = emf across galvanometer e =
Sensitivity of galvanometer,
θ
Sensitivity of the Bridge
A V IR RV I VR R Iv Ra A V IR RV Va VR R
Measurement of High Resistance Loss of charge method
R =
V S1 V C S2 R V -