XII Physics BIEK Chapter 15 - Electrical Measuring Instruments

ELECTRICAL MEASURING INSTRUMENTS
THE MOVING COIL GALVANOMETER
The moving coil galvanometer is a basic electrical instrument. It is used for the detection or measurement of small currents.


Principle

When current flows in a rectangular coil placed in a magnetic field it experience a magnetic torque due to which it rotates through an angle proportional to the current flowing through it.

Construction:

The essential parts of a moving coil galvanometer are

1. A U-shaped permanent magnet with cylindrical concave pole-pieces.

2. A flat coil of thin enamel Insulated wire (usually rectangular)

3. A soft iron cylinder

4. A scalar lamp and scale arrangement.


In suspended type or D Arsonvals galvanometer the flat rectangular coil of thin enamel insulated wire of suitable number of terms wound on a light non-metallic or non-magnetic (brass or aluminum) frame is suspected between the cylindrical concave pole pieces of the permanent U-shaped magnet by a thin phosphor-bronze strip. One end of the wire of the soil is soldered to strip. The other end of the strip is fixed to the frame of the galvanometer and connected to an external terminal. It serves as one current lead. The other end of the wire of the coil is soldered to a loose and soft spiral of wire connected to another external terminal. The soft spiral of wire serves as the other current lead. A soft iron cylinder, coaxial with the pole-pieces is placed within the frame of the coil but quite detached from it and is fixed to the body of the galvanometer. In the space between it and the pole pieces, where the coil moves freely, the soft iron cylinder makes the field stronger and radial so that the magnetic field is always parallel to the plane of the coil. To note the deflection a concave mirror along with lamp and scale arrangement is used.

Working

When a current passes through the galvanometer coil, it experiences a magnetic deflecting torque, which tends to rotate it from its rest position. As the coil rotates it produces a twist in the suspension strip. The coil rotate until the elastic restoring torque due to which the strip does not equalize and cancel the deflecting magnetic torque and then it attains equilibrium and stops rotating further.

i.e. Deflecting torque = Restoring torque

But deflecting torque = BINA Cos α

BINA Cos α = c0

Where B = strength of the magnetic field

I = current in the coil

A = Area of the coil

N = Number of turns in the coil

θ = Angle of twist of the suspension strip

c = torque per unit twist of the suspension strip for the equilibrium

As c/BNA is constant.

In pivoted type or Weston galvanometer the coil instead or being suspended by a strip is pivoted between two jeweled bearings. The restoring torque is provided two hair springs one on either side of the coil and curling on the opposite sense are connected one to each spring. The hairspring thus also serve as current leads to the coil. A light aluminum pointer is fixed to the coil, which moves over a calibrated circular scale with equal divisions, which measures the deflection directly.


Current Sensitivity of a Galvanometer

A galvanometer is said to be sensitive if for a small current the deflection "θ" is sufficiently large. A galvanometer can be made more sensitive if c/BNA is made small. Thus to increase sensitivity "c" may be decreased or B, N and A may be increased "C" can be decreased by increasing the length of suspension wire or by decreasing its can be decreased by increasing the length of suspension wire or by decreasing its diameter, but this process cannot be taken too far < as the suspension must be strong enough to carry the coil. "N" or "A" cannot be increased because it makes the coil heavy. The loss of sensitivity due to the use of fewer turns is however made us by the very high value of the magnetic field employed.

The current sensitivity of a galvanometer is usually defined as the current in microampere required to cause one-millimeter deflection on a scale place 1.0 meter from the mirror of the galvanometer.




THE AMMETER
Ammeter is an instrument, which is used for measuring electric current. A galvanometer can measure small current if its scale is calibrated for the current. For the measurement of large current a bypass resistance called a shunt, of appropriate small value is connected in parallel with the galvanometer coil. This resistance allows the large excess current through itself while a fraction of the current passes through the galvanometer coil. The scale of the instrument is so calibrated that it can measure the main current directly.

Consider a galvanometer "G" whose resistance is "Rg" and which gives full scale deflection when current "Ig" flows through it to convert the galvanometer into an ammeter which can measure a maximum current "I" a shunt "Rs" of appropriate small resistance should be connected in parallel with the galvanometer such that the current "Ig" must flow through the galvanometer coil.

The potential difference "Vg" across the galvanometer is given by

Vg = Ig Rg

The potential difference "Vs" across the shunt is given by

Vs = Is Rs = (I - Ig) Rs

Where Is = I - Ig = current through the shunt.

As "Rg" and "Rs" are connected in parallel to each other therefore potential difference across them will be equal i.e.

Vs = Vg

(I - Ig) Rs = Ig Rg

Rs = Ig Rg / I - Ig

Ammeter is always connected in series with the circuit.


Multi Range Ammeter

Sometimes an ammeter has more than one range, which means that it has as many different shunts as the ranges. The desired range is selected by insertion the proper shunt in position. In one type, one end of each shunt is permanently connected to a common terminal while the other end of each is connected through a range to a second common terminal.




THE VOLTMETER
Voltmeter is an instrument which is used for measuring potential difference between any two points of a current carrying (or between the two terminals of a source of emf). A galvanometer can be used for measuring a very small Potential Difference. If its scale is calibrated for voltage. For the measurement of large potential difference. A high resistance of the order of Kilo-ohms is connected in series with it. This resistance is commonly known as "Multiplier Resistance".

Consider a galvanometer "G" where resistance is "Rg" and which deflects full scale for the current "Ig" to convert this galvanometer into a voltmeter measuring a Potential difference upto "V" volts. An appropriate high resistance "Rn" must be connected in series with it such that for the potential difference "V" applied between the ends of the above combination. The current "Ig" must flow through the galvanometer. However the total resistance between the terminal a & b is Rn + Rg.

(Rn + Rg+ Ig = V

Rn + Rg = V / Ig

Rn = V / Ig - Rg

Voltmeter is always connected in parallel with the circuit.


Multirange Voltmeter

Sometimes a voltmeter has more than one range, which means it has as many different resistance as the ranges. The desired range is selected by inserting the proper resistance in position.

We have a common terminal marked (+) and as many other terminals as the ranges. In the other type one terminal is common marked (+) while the different range terminals can be connected by a range switch to the other common terminals.




WHEAT STONE BRIDGE
If four resistances R1, R2, R3 and R4 are connected end to end in order to form a closed mesh ABCDA and between one pair of opposite junctions. A and C cell is connected through a key K1 while between the pair of opposite junctions B and D a sensitive galvanometer "G" is connected through another key K2. The circuit so formed is called a "Wheatstone-bridge".

In the above bridge if the key is closed first, some current flows through the cell and the resistance R1, R2, R3 and R4. If the key K2 is also closed the current will usually be found to flow through the galvanometer indicated by its deflection. However if the resistance R1, R2, R3 and R4 (or at least one of them) are adjusted, a condition can always be attached in which the galvanometer show no deflection at all i.e. no current passes through it. Then the potential difference between B & D must be zero i.e. B & D must be at the same potential. This implies that

P.d. between A and B = p.d. between A and D

OR

V(AB) = V(AD)

P.d. between B and C = p.d. between D and C

OR

V(bt) = V(Dt)

Since no current flows through the galvanometer the current R1 equals that in R2, say II and the current in R3 equals that in R4 say 12

As,

V(AB) = V(AD)

1(1) R(1) = 1(2) R(3) -------- (I)

Also,

V(BC) = V(DC)

1(1) R(2) = 1(2) R(4) --------- (II)

Dividing eq 1 by eq 2

1(1) R(1) / 1(1) R(1) = 1(1) R(1) / 1(1) R(1)

R(1) / R(1) = R(1) / R(1)

Under balanced condition if any three resistance are known then the fourth can be found easily (i.e. wheatstone principle).

The wheatstone principle is used in Meter Bridge, the P.O. box Carey Foster's Bridge, Callender and Graffite's Bridge etc.




METER BRIDGE
The Meter Bridge also called slide - Wire Bridge is an instrument based on wheatstone principle. It consists of a long thick copper strip bent twice at right angles. Two small portions are cut off from it near the bends to provide the gaps across which two resistances are known one and an unknown may be connected. Each of the three pieces of the strip is provided with binding screws. A uniform wire (of magnetic or other) one meter long and of fairly high resistance is stretched, along the side a meter scale is connected to the ends of the strip.

For measuring an unknown resistance "X" it is connected in one gap of the Meter Bridge and a standard resistance box "R" is connected in the other gap. A cell and a galvanometer are connected. The jockey "J" is moved along the wire to obtain the balance point D. Under balanced condition if the length of the wire segment. A D toward X is Lx and the length of the wire segment CD towards R is L(R) then their resistances are ρL(R) respectively.

Where ρ = resistance per unit length of the wire.




POST OFFICE BOX [P.O BOX]
Post Office Box is an instrument, which is based on wheatstone principle. It was first introduced for finding resistance of telegraph wires and for fault - findings work in the post and telegraph office that's why it is called "Post Office Box". It is more compact and easier to use.

It consists of three sets of resistances P, Q and R. The arms P and Q called the ratio arms, usually consists of three resistances each viz. 10, 100 and 1000 ohms so that any decimal ratio from 1:100 to 100:1 may be used. The third arm "R" is an ordinary set of resistances. The unknown resistances "X" to be measured forms the fourth arm. Introducing the ratios 1:1, 10:1, 100:1 in turn the balance or null position is traced by adjusting "R". Balance is usually obtained at the ratio 100:1 for some value of "R". With this value of "R" the value of X can be easily be calculated using relation of Wheatstone bridge i.e.

P/Q = R/X

X = R Q/P




THE OHMMETER
The ohmmeter is a device used for the measurement of resistance. It consists of a sensitive galvanometer "G", adjustable resister "R" and a torch cell "E" connected in series between two terminals A and B. The unknown resistance "X" to be measured is connected between the terminals A and B. The resistance R is so chosen that when the terminals A and B are short circuited (i.e. X = 0). The galvanometer gives full-scale deflection when no connection is between A and B (i.e. X = ∞). The galvanometer shows zero deflection for the value of X between = and ∞. The deflection is small or large depending on the value of X. The scale of the galvanometer is calibrated with different known values of X and there the circuit serves as an ohmmeter to measure any unknown resistance approx. The scale of the ohmmeter however is not linear.

Using different conditions of R is series and different shunts across the galvanometer worked by range switches, the ohmmeter can be adopted for different accessories for e.g. 1 Ω accuracy in tens of ohms, in hundreds of ohms, in thousands of ohms, in mega ohms etc. Ohmmeter is not a very accurate instrument.

POTENTIOMETER
Potentiometer is device for measuring the p.d (voltage) between two points of a circuit or the e.m.f of a current source. It consists of a uniform wire stretched on a wooden board along a meter scale.

Consider a uniform resistance wire AB of length L and Resistance R, across which is connected to a source of constant EMF (e.g. an accumulator) through a key and a rheostat to adjust and maintain a constant current 1 through it.

As the current flows, the P.d. between A and B = V(AB) = IR

If one terminal of a wire is connected to A while other is moved on the wire AB then instrument acts as a Potential Divider.

To find an unknown EMF of a cell or some other potential difference or the ratio of the emf of two cells consider the circuit. The positive terminals of a cell of unknown EMF "E(N)" and a standard cell of Emf E(N) are connected to the terminal A. The negative terminals of both the cells are joint to the jockey through a two way key and a sensitive galvanometer. Using the two-way key first cell E(N) only is introduced into the galvanometer branch and balanced point C and length L are found for it.




THE AVO-METER
An Avo-meter is an apparatus which is used to measure current, voltage and resistance in other words it is an ampere, volts and ohms. It can measure direct as well as alternative voltage and currents. It consists of a galvanometer with different scales graduated in such a way that all the three quantities can be measured. A selector-cum-range switch is provided. Its has its own battery. A rectifier is also included in the instrument to convert A.C. into D.C. before they pass through the Galvanometer.