Figure 1: Hay’s Bridge.

The schematic of Hay’s bridge is shown in Fig. 1. Hay’s bridge differs from Maxwell’s bridge by having a resistance R₁ in series with a capacitor C_l instead of being parallel.

For large phase angles, R₁ needs to be low; therefore this bridge is more convenient for measuring high Q coils. For Q =10, the error is ± 1% and for Q = 30, the error is ± 0.1%.

When bridge is balanced,

\[{{Z}_{1}}{{Z}_{x}}=\text{ }{{Z}_{2}}{{Z}_{3}}\text{            }……\left( 1 \right)\]

\[{{Z}_{1}}={{R}_{1}}-\frac{j}{\omega {{C}_{1}}}\]

\[{{Z}_{2}}={{R}_{2}}\]

\[{{Z}_{3}}={{R}_{3}}\]

\[{{Z}_{x}}={{R}_{x}}+j\omega {{L}_{x}}\]

From equation (1),

\[\left( {{R}_{1}}-\frac{j}{\omega {{C}_{1}}} \right)\left( {{R}_{x}}+j\omega {{L}_{x}} \right)={{R}_{2}}{{R}_{3}}\]

\[{{R}_{1}}{{R}_{x}}+j\omega {{L}_{x}}{{R}_{x}}-\frac{j{{R}_{x}}}{\omega {{C}_{1}}}+\frac{{{L}_{x}}}{{{C}_{1}}}={{R}_{2}}{{R}_{3}}\]

\[\left( {{R}_{1}}{{R}_{x}}+\frac{{{L}_{x}}}{{{C}_{1}}} \right)+j\left( \omega {{L}_{x}}{{R}_{1}}-\frac{{{R}_{x}}}{\omega {{C}_{1}}} \right)={{R}_{2}}{{R}_{3}}\]

Equation real and imaginary terms

\[{{R}_{1}}{{R}_{x}}+\frac{{{L}_{x}}}{{{C}_{1}}}={{R}_{2}}{{R}_{3}}\text{ }…\left( 2 \right)\]

\[\omega {{L}_{x}}{{R}_{1}}-\frac{{{R}_{x}}}{\omega {{C}_{1}}}=0…\left( 3 \right)\]

Thus,

\[{{L}_{x}}=\frac{{{R}_{x}}}{{{\omega }^{2}}{{R}_{1}}{{C}_{1}}}\]

Substituting Equation (3) in equation (2)

\[{{R}_{1}}{{R}_{x}}+\frac{{{R}_{x}}}{{{\omega }^{2}}{{R}_{1}}C_{1}^{2}}={{R}_{2}}{{R}_{3}}\]

\[{{R}_{x}}\left[ {{R}_{1}}+\frac{1}{{{\omega }^{2}}{{R}_{1}}C_{1}^{2}} \right]={{R}_{2}}{{R}_{3}}\]

\[{{R}_{x}}\left[ \frac{{{\omega }^{2}}R_{1}^{2}C_{1}^{2}+1}{{{\omega }^{2}}{{R}_{1}}C_{1}^{2}} \right]={{R}_{2}}{{R}_{3}}\]

\[{{R}_{x}}=\frac{{{\omega }^{2}}C_{1}^{2}{{R}_{1}}{{R}_{2}}{{R}_{3}}}{1+{{\omega }^{2}}R_{1}^{2}C_{1}^{2}}…\left( 4 \right)\]

Substitution Equation (4) in equation (3)

\[{{L}_{x}}=\frac{{{\omega }^{2}}C_{1}^{2}{{R}_{1}}{{R}_{2}}{{R}_{3}}\text{ }}{\left( 1+{{\omega }^{2}}C_{1}^{2}R_{1}^{2} \right)\left( {{\omega }^{2}}{{C}_{1}}{{R}_{1}} \right)}\]

\[{{L}_{x}}=\frac{{{C}_{1}}{{R}_{2}}{{R}_{3}}\text{ }}{\left( 1+{{\omega }^{2}}C_{1}^{2}R_{1}^{2} \right)}…\left( 5 \right)\]

From Equation (5) unknown inductance can be calculated.

As ω appears in the expression for L_x, this bridge is frequency sensitive.

Quality factor (Q) for capacitor is

\[\omega {{L}_{x}}{{R}_{1}}-\frac{{{R}_{x}}}{\omega {{C}_{1}}}=0\text{          }\]

∴\[\text{  }\omega {{C}_{1}}{{R}_{1}}=\frac{1}{Q}\text{   }….\left( 6 \right)\]

Substituting Equation (6) in Equation (5)

\[{{L}_{x}}=\frac{{{C}_{1}}{{R}_{1}}{{R}_{3}}}{1+\frac{1}{{{Q}^{2}}}}\]

For a value of Q greater than 10, the term 1/Q² will be smaller than 1/100 and therefore can be neglected.

L_x = C₁R₂R₃ (for Q >10)

Thus for Q > 10, the equation obtained for L_x in Hay’s bridge is same as that in Maxwell’s bridge.

For inductors with Q less than 10, the 1/Q² term can not be neglected. Hence this bridge is not suited for measurement of inductors having Q less than 10.

For measuring inductance using Hay’s bridge, unknown inductance is connected in one of the arms of Hay’s bridge and resistors R₁ and R₃ are adjusted to obtain balance of the bridge. Then using the Equation (5), unknown inductance can be calculated.

Advantages of Hay’s Bridge

1. It can measure inductances with high Q i.e. Q > 10.
2. A commercial bridge measures inductance from 1 μH to 100 H with ± 2% error.
3. It can be used for measuring incremental inductance.

Disadvantages of Hay’s Bridge

1. The unknown value of inductance depends on loss of inductor (Q) and also on operating frequency.
2. It can not measure inductance with low Q i.e. Q < 10.

The post What is Hay’s Bridge? Circuit Diagram, Derivation & Advantages appeared first on Electrical and Electronics Blog.

Figure 1: Maxwell’s Bridge.

When bridge is balanced,

\[{{Z}_{1}{Z}_{x}}={{Z}_{2}{Z}_{3}}\]

 \[{{Z}_{x}}=\frac{{{Z}_{2}}{{Z}_{3}}}{{{Z}_{1}}}={{Z}_{2}}{{Z}_{3}}{{Y}_{1}}\text{            }……\left( 1 \right)\]

\[{{Z}_{1}}={{R}_{1}}\parallel \frac{1}{j\omega {{C}_{1}}}\]

\[{{Y}_{1}}=\frac{1}{{{R}_{1}}}+j\omega {{C}_{1}}\]

\[{{Z}_{2}}={{R}_{2}}\]

\[{{Z}_{3}}={{R}_{3}}\]

\[{{Z}_{x}}={{Z}_{x}}+j\omega {{L}_{x}}\]

From Equation (1) we have,

\[{{R}_{x}}+j\omega {{L}_{x}}={{R}_{2}}{{R}_{3}}\left( \frac{1}{{{R}_{1}}}+j\omega {{C}_{1}} \right)\]

\[{{R}_{x}}+j\omega {{L}_{x}}=\frac{{{R}_{2}}{{R}_{3}}}{{{R}_{1}}}+j\omega {{R}_{2}}{{R}_{3}}{{C}_{1}}\]

Equation real and imaginary terms,

\[{{R}_{x}}=\frac{{{R}_{2}}{{R}_{3}}}{{{R}_{1}}}\]

And  \[{{L}_{x}}={{R}_{2}}{{R}_{3}}{{C}_{1}}\text{            }……\left( 2 \right)\]

Thus the measurement of unknown inductance is independent of the excitation frequency. The scale of the resistance can be calibrated to read inductance directly.

Quality factor (Q) for inductance is,

\[Q=\frac{\omega {{L}_{x}}}{{{R}_{x}}}=\frac{\omega {{C}_{1}}{{R}_{2}}{{R}_{3}}\times {{R}_{1}}}{{{R}_{2}}{{R}_{3}}}=\omega {{C}_{1}}{{R}_{1}}\]

For high values of Q, R₁ becomes excessively large and it is impractical to obtain a satisfactory variable standard resistance in the range. Therefore Maxwell’s bridge is suitable for measurement of inductance with low Q values.

For measurement of inductance using Maxwell’s bridge, unknown inductor is connected in one of the arms and resistor R₁ and R₃ is adjusted to balance the bridge. Then using the derived Equation (2), unknown inductance can be calculated.

Advantages of Maxwell’s Bridge

1. This bridge is particularly suited for inductance measurement as comparison with capacitor is more ideal than with another inductor.
2. It can measure inductors with high Q.
3. It can measure inductance from 1 H to 1000 H with ± 2% error.
4. The measurement is independent of excitation frequency

Disadvantages of Maxwell’s Bridge

1. It cannot be used for measuring inductance with high Q values.
2. Due to fixed capacitor, there is an interaction between the resistance and reactance balances. This can be avoided by varying the capacitor instead of R₁ and R₃.

The post What is Maxwell’s Bridge? Circuit Diagram, Derivation & Advantages appeared first on Electrical and Electronics Blog.

Figure 1: DC Voltmeter.

The DC Voltmeter is an electrical measuring instrument which is used to measure line potential difference (P.D) between two points. The voltage to be measured be DC. Basic Connection Diagram of DC Voltmeter is shown in Fig. 1.

R_m – multiplier resistance connected in series with voltmeter coil having its own resistance

Range Extension of Voltmeter by Multiplier

Range extension of voltmeter means increasing the capacity of same voltmeter to measure higher values of voltages safely.

Need of range extension of Voltmeter

Voltmeter range extension voltmeter coil is thin and delicate and it can withstand for small voltages applied across it so voltmeter cannot be used directly if high voltage is to be measured.

How voltmeter range is extended?

Figure 2: DC Voltmeter with multiplier.

A high resistance called as multiplier is connected in series with voltmeter when it is used for high voltage measurement (see Figure 2). Multiplier creates major voltage drop across it and remaining voltage of safe value gets applied to the voltmeter. The requirements of multiplier are same as that of shunt.

Let

I_V = current producing full scale deflection.

R_m = resistance of multiplier Ω.

v = voltage across voltmeter in volts

V = high voltage to be measured in volts

\[v={{I}_{v}}{{R}_{v}}\]

\[V={{I}_{v}}\left( {{R}_{m}}+{{R}_{v}} \right)\]

\[V-{{I}_{v}}{{R}_{v}}={{I}_{v}}{{R}_{m}}\]

\[{{R}_{m}}=\frac{V-{{I}_{v}}{{R}_{v}}}{{{I}_{v}}}\]

\[{{R}_{m}}=\frac{V}{{{I}_{v}}}-{{R}_{v}}\]

Multiplying power of multiplier is given by,

\[m=\frac{V}{v}=\frac{{{I}_{v}}\left( {{R}_{m}}+{{R}_{v}} \right)}{{{I}_{v}}{{R}_{v}}}=\frac{{{I}_{v}}{{R}_{m}}+{{I}_{v}}{{R}_{v}}}{{{I}_{v}}{{R}_{v}}}\]

\[=1+\frac{{{R}_{m}}}{{{R}_{v}}}\] \[{{R}_{m}}=\left( m-1 \right){{R}_{v}}\]

Multirange Voltmeter

• Using individual multiplier

Figure 3.

• Using universal multiplier or potential divider 

Figure 4.

Separate multipliers can be used for different ranges of voltage. Fig. 2 shows 4 multipliers. The respective multiplier is selected by operating selective switch in Fig. 4 a single multiplier known as universal multiplier is shown tapping’s are provided on the multiplier.

Disadvantages of Multipliers

The multipliers can be used safely upto 1000 volts beyond this value it is not applicable because of following reasons :

1. Power consumption increases as voltage increases.

\[P=\frac{{{V}^{2}}}{{{R}_{m}}}\]

2. Construction of multipliers used for high voltage are costly and difficult.

The post What is DC Voltmeter? Working, Circuit Diagram & Multirange appeared first on Electrical and Electronics Blog.

Figure 1: PMMC Instrument.

Working Principle of PMMC Instrument

When a current carrying conductor is placed in a magnetic field the force is produced on the conductor (coil). This force tends to move the coil in the space.

Construction of PMMC Instrument

Fig. 1 shows constructional details of PMMC instruments with different constructions of permanent magnets. A coil is wound on aluminium former which is supported by spindle, the two ends of spindle are supported by Jewel bearings. Iron cylinder is placed inside the coil and this assembly is surrounded by permanent magnet coil carries current to be measured.  The current is fed into and taken into from coil from springs, flexible ligaments are provided to make provision for this connection. Deflecting torque is produced as described in the working principle. Controlling torque is achieved with springs and damping torque is provided with the help of aluminium former. The iron cylinder (core) minimizes fringing effect and concentrates the flux in the region near coil sides. The iron cylinder makes the orientation of magnetic field radial. Deflection is observed at the pointer dial. The defecting torque (T_d) is directly proportional to current hence scale is uniform.

PMMC Instrument Parts, Material and their Functions

Suitability of PMMC Instrument

This instrument is suitable for DC measurements only. If it is connected to ac supply the direction of alternating torque alters every half cycle and moving system cannot cop up with such rapid variations. So pointer stays at zero position.

Advantages of PMMC Instrument

• Deflection is proportional to current,

\[{{T}_{d}}\propto l\]

Therefore scale is uniformly divided.

• Power consumption is very low.
• High accuracy due to high torque to weight ratio.
• Sensitivity is high because of strong magnetic flux. Errors due to stray magnetic field are small because operating magnetic field is strong.
• It is free from hysteresis and stray magnetic field errors.
• Uses effective damping method. (eddy current damping)
• Single instrument can be used for different current and voltage ranges using shunt and multiplier.
• Torque to weight ratio of moving system is high.

Disadvantages of PMMC Instrument

1. Suitable for DC measurements only.
2. Cost is higher than moving iron instrument.
3. Strength of permanent magnet decreases due to ageing.
4. Delicate construction, so to be used with care.
5. Thermo-electric EMF may cause errors when it is used with shunts. 2.3.1(C)

Derivation of Torque Equation of PMMC Instrument

l – Length of the coil in meters

B — Flux density in air gap in Tesla

d – Width of coil in meters

i – Current through moving coil in Amp

k – Spring constant in Nm/rad

θ – Final state deflection in rad

α – Angle between direction of magnetic field and velocity vector of moving coil for radial field.

Expression for force on each coil side given by,

\[=N\text{ }Bi\text{ }l\text{ sin }\alpha \]

Due to radial flux the coil cuts flux at 90º always

\[\alpha =90{}^\circ \] \[\text{Force = }N\text{ }Bi\text{ }l\text{        }……..\text{since }\alpha =90{}^\circ \]

Deflecting torque

\[{{T}_{d}}=\left( N\text{ }Bi\text{ }l \right)\times \left( d \right)=N\text{ Bi A        }…\left( A=l\times d \right)\]

N, B, A are constants in instrument

\[{{T}_{d}}=N\text{ B Ai = Gi}\]

Where,

G = NBA known as displacement constant

Controlling torque is provided by means of spring,

\[{{T}_{c}}=k\theta \]

Where k is spring constant unit : Nm / rad

\[\theta =\text{ Final steady deflection in rad}\text{.}\]

At final steady deflection

\[{{T}_{c}}={{T}_{d}}\text{         } k\theta \text{ }=\text{ }Gi\] \[\theta =\frac{Gi}{k}\]

Thus deflection is proportional to i that is why scale is uniform.

The post What is Permanent Magnet Moving Coil (PMMC) Instrument? Working Principle, Diagram, Construction, Parts and Derivation appeared first on Electrical and Electronics Blog.

Functions of Controlling Torque

1. It produces an equal torque in opposite direction to deflecting torque. Thus the deflection is proportional to quantity under measurements.
2. It brings back to pointer to zero position when deflecting torque becomes zero.

The pointer shows final steady state deflection when Controlling torque equals to the Deflecting torque, i.e.

\[{{T}_{C}}={{T}_{d}} \]

Torque to Weight Ratio (T/W Ratio) :

The moving system of measuring instrument should be light in weight. If it is heavy, it will produce more friction torque during deflection of the instrument and thus performance of the instrument is hampered. So if friction torque is large, the instrument may not show deflection for small magnitude quantities. i.e. its sensitivity is affected. If friction torque is negligible, the instrument can show appreciable deflection for small magnitude quantities.

\[\text{Hence the ratio = }\frac{\text{Deflecting torque}}{\text{Frictional torque}}\]

Since frictional torque depends on weight of moving system the ratio can be written as,

\[\frac{\text{Deflecting torque}}{\text{Weight of moving system}}=\frac{\text{Torque}}{\text{Weight}}=\frac{T}{W}\]

More is the \(\frac{T}{W}\) ratio, better is the performance of the instrument.

Methods of Providing Controlling Torque

Following methods are used to provide controlling torque :

1. Spring control
2. Gravity control

Spring Control

This method is commonly employed in indicating instruments. A spiral wound spring made up of phosphor bronze is attached to the spindle as shown in Fig. 1. One inner end of spring is attached to the spindle and outer end is attached to a fixed point or support on the instrument. A jewel screw is provided for adjustment of spring tension i.e. for adjusting controlling torque (T_c). The jewel screw is also operated for zero adjustment. In many indicating instruments, the spring is a current carrying member. i.e. it provides lead for incoming and outgoing current. The spring also produces controlling torque. So both electrical and mechanical properties of spring are important.

Desired properties of Spring

1. It should be non magnetic.
2. It should withstand mechanical vibrations.
3.  It should have low temperature coefficient of resistance (if it is a current carrying member).
4. It should not deteriorate with time.

Phosphor bronze material is best suited for springs. The controlling torque.

\[{{T}_{c}}=k\theta \]

Where,

k – Spring constant

θ – Angular deflection of pointer in radian from zero position

The expression for controlling torque in terms of physical parameters of the spring is as follows :

\[{{T}_{c}}=\frac{Eb{{t}^{3}}}{12l}\theta \]

E – Young’s modulus of spring material in N/m².

b – Width of spring in meter

t – Thickness of spring in meter

l – Length of spring in meter

θ – Angular deflection in rad

\[{{T}_{c}}=k\theta \] \[k=\frac{Eb{{t}^{3}}}{12l}\]

Where, k is spring constant.

Advantages of Spring Control

1. Spring control is easy to apply.
2. The spring material is non magnetic so it does not affect the operating flux.
3. The position of instrument does not affect controlling torque. So instrument can be operated in horizontal or vertical position.
4. It is light in weight so does not add to weight of the instrument.
5. Cost is less.
6. T_c = k θ so controlling torque equation is linear.
7. Maintenance is easy.
8. Adjustment of controlling torque is easy.

Disadvantages of Spring Control

1. Deformation : If spring is stretched beyond its limit it may loose its elastic properties.
2. If temperature variation is drastic, it will affect controlling torque.

Gravity Control

Figure 2.

It uses gravity force to produce controlling torque. Control weight and balancing weight are attached to the spindle as shown in figure 2. The balancing weight is provided for mechanical balance and for zero setting. The control and balancing weight are adjustable this can be taken towards the spindle or away from the spindle. Threads are provided for this purpose.

Controlling Torque = W Sinθ

Advantages of Gravity control

1. No effect of temperature.
2. Effective method of controlling torque.
3. Adjustment can be done easily.
4. Longer life.

Disadvantages of Gravity control

1. It has to be used in vertical position only so suitable for vertically mounted instruments.
2. Control weight adds to the weight of moving system. Costly.
3. Longer life.
4. Maintenance is complicated

Difference between Spring Control and Gravity Control

The post What is Controlling Torque? Methods, Diagram & Formula appeared first on Electrical and Electronics Blog.

Figure 1: Wheatstone Bridge.

Wheatstone bridge has its own importance and it is used from the very old days and proves to be important and reliable even today for measurement of unknown resistance by comparison method.

Construction of Wheatstone Bridge

In its simplest form, it has 4-arms connected in diamond shape. 3-arms have the resistances P, Q and S and R arm for connecting unknown resistance whose value is to be determined.  S-resistance is adjustable variable resistance and P and Q are the ratio arms of multiple value resistances 10, 100, 1000,………

These 4-arms are connected at the junctions ABC and source voltage (Battery of 1.5 Volts) is connected across A and C. Galvanometer is connected across terminals B and D.

Steps in Wheatstone Bridge Balancing and Balancing Equation

Battery and galvanometer are connected as shown in the circuits unknown resistance R is connected across X₁ X₂ key (or switch S) is pressed to commence (see Figure 1). The values of P and Q ratio are selected. Resistance ‘S’ is varied. Initially the currents in branch are different as I₁, I₂, I₃ and I₄ and also galvanometer deflects in either direction. P, Q and ‘S’ are so adjusted that galvanometer shows zero (Null-point) reading. This condition is known as balanced condition or null condition of bridge. In balanced condition, current in the upper two branches through P and Q is same and in the lower branches through R and S is same. When there is no current in the galvanometer the points B and D are equipotential points.

Potential difference across AB = Potential difference across AD

\[{{I}_{1}}P={{I}_{2}}R….(1)\]

Also, Potential difference across BC = Potential difference across CD

\[{{I}_{3}}Q={{I}_{4}}S….(2)\]

Current in the upper branch will be same throughout say I_l and current in the lower branch will be same throughout say I₂.

\[{{I}_{3}}={{I}_{1}}\]

\[\text{And }{{I}_{4}}={{I}_{2}}\]

\[{{I}_{1}}P={{I}_{2}}P….(3)\]

\[\text{And }{{I}_{1}}Q={{I}_{2}}S….(4)\]

Dividing equation (1) by equation (3),

\[\frac{{{I}_{1}}P}{{{I}_{1}}Q}=\frac{{{I}_{2}}R}{{{I}_{2}}S}\]

\[\frac{P}{Q}=\frac{R}{S}\]

\[\text{Unknown resistance }R=S\times \frac{P}{Q}\]

This is the equation of Wheat stone bridge at balance. Thus unknown resistance R is found from ratio arm resistance P and Q and variable resistance S.

Figure 2: Control panel of Wheatstone Bridge.

Resistances P, Q and S are mounted inside Wheatstone bridge box with adjusting knobs on the box-plate (see Figure 2) for operation. P and Q normally consistence of 4-resistors each, the values being 10, 100, 1000, 10000. Resistor ‘S’ consists of a 4-dial or 5 dial decade arrangement of resistors.

Errors Present in Wheatstone Bridge or Limitations / Disadvantages of Wheatstone Bridge :

Following errors are present in Wheatstone bridge :

Errors Present in Wheatstone Bridge,

1. Contact resistance
2. Thermoelectric
3. Effect of temperature
4. Other errors

1. Contact resistance

This can cause serious error when comparatively low resistance is measured. If the contact resistance of connecting leads, terminals is greater than the unknown resistance, a serious error is introduced.

2. Thermoelectric emf

Thermo electric emfs are present in the measuring circuit which cause error.

3. Effect of temperature

The standard resistances used in the bridge circuit may suffer from temperature variations. This happens because of self heating effect (IR). E.g. If resistances in the bridge are wire wound resistances and made up of copper, with temperature coefficient of 0.004/ºC. Thus if temperature changes by 1ºC the error caused is 0.4%.

4. Other errors

The bridge should be precisely balanced so if human error is involved, there will be error in measurement. The galvanometer used should be sensitive otherwise null condition cannot be detected accurately.

The post What is Wheatstone Bridge? Working Principle, Construction, Derivation, Diagram & Formula appeared first on Electrical and Electronics Blog.

Figure 1: Capacitance Level Sensor.

Working Principle of Capacitance Level Sensor

The capacitance method of liquid level measurement or Capacitance Level Sensor operates on the principle of parallel plate capacitor, which can be stated as the capacitance of the parallel plate capacitor varies or changes if the area or dielectric constant of it changes.

Construction and Working of Capacitance Level Sensor

The capacitance probe or element is placed inside the tank (generally near to its wall) whose level of liquid is to be measured. The liquid (whose level is to be measured) placed inside the tank can be of two types one is conductive type and the other is nonconductive type. If the liquid is conductive in nature then the capacitance probe acts as one plate of the capacitor whereas the liquid acts as another plate of the capacitor. The dielectric material between these two plates is nothing but the insulation provided for the capacitance probe. In this case, the capacitance varies as the height of the liquid changes i.e., the principle of change in area of plates is used. Therefore when the height of the liquid increases the area between the plates decreases and output capacitance increases. Similarly when the height decreases the capacitance also decreases. In case the liquid whose level is to be measured is nonconductive in nature then the probe acts as one plate of the capacitor whereas the wall of the metal tank acts as another plate of the capacitor. In this case, the dielectric material is liquid. Here the capacitance varies as the dielectric material change (i.e., the principle of change in dielectric constant is used).

As shown in figure 1, the capacitance meter is connected to the capacitance probe and to the wall of the tank. The capacitance meter is calibrated interns of liquid level. If the level of the liquid inside the tank is low (or decreased) the capacitance of the capacitor decreases. The decreased capacitance value is displayed on the capacitance meter.

Similarly the capacitance increase with increase of liquid level and is indicated by the meter which intern indicates the level of the liquid inside the tank.

Advantages of Capacitance Level Sensor

1. This method of level measurement is very sensitive.
2. This method can be used for small systems.
3. No problem of wear-tear since it does not contain any movable pans.
4. It can be used with slurry fluids.

Disadvantages of Capacitance Level Sensor

1. The performance will be affected by the change in temperature.
2. The connection and mounting of metal tank with the meter should be proper, otherwise some errors may occur.

The post What is Capacitance Level Sensor? Working Principle, Diagram, Construction & Advantages appeared first on Electrical and Electronics Blog.

Working & Construction of Eddy Current Tachometer

The eddy current tachometer consists of a permanent magnet. Here two pole or multiple-pole magnets can be used. This magnet is arranged to a shaft. The shaft is used to make contact with the rotor whose angular velocity is to be measured. An eddy current cup which is nothing but a conducting material is placed near to the magnet. This is carried by a spindle arrangement and restrained by using torsion spring. Mostly aluminium is used to make eddy current cup. When the shaft is in contact with a rotor (which is rotating), the shaft rotates along with magnet.

Due to this, flux passes through the cup. With the change in the rotation of the magnet the direction of induced flux also changes causing the alternate flux density (B) to develop in the cup. So an electric field is produced with the rate of change of flux density B.

\[ \text{Curl E = }\frac{-dB}{dt}\]

This electric field will generate eddy current in the shell of the cup. The generated eddy current density is indicated by J and it will produces a secondary magnetic field of intensity H. The relation between magnetic field of intensity H and eddy current density J is given by,

\[\text{Curl H = J}\]

Due to these two magnetic fields a torque is generated in the eddy current cup, which is proportional to the angular speed. A pointer scale arrangement is provided at the back of the spindle. If the eddy current cup is restrained by torsion spring, an angular deflection of spindle occurs and is indicated over a calibrated scale. If both magnetic torque and spring torque are balanced then it will be indicated by pointer.

Applications of Eddy Current Tachometer

Eddy current tachometers are used,

1. In automobile speedometers
2. To measure speed in aircraft engines
3. To measure locomotive speeds
4. In control systems and industrial applications.

The post What is Eddy Current Tachometer? Working Principle, Diagram, Construction & Applications appeared first on Electrical and Electronics Blog.

Working Principle of Ultrasonic Flow Meter

The velocity of propagation of ultrasonic sound waves in fluid changes when the velocity of the flow of fluid changes.

Working & Construction of Ultrasonic Flow Meter

The arrangement of flow rate measurement using ultrasonic transducer contains two piezoelectric crystals placed in the fluid (gas or liquid) whose flow rate is to be measured. Of these two crystals, one acts as a transmitting transducer (transmitter, T) and the other acts as a receiving transducer (receiver, R). The transmitter and thevreceiver are separated by some distance, say d. Generally, the transmitting transducer is placed in the up stream and it transmits ultrasonic pulses when an electronic oscillator energizes it. These ultrasonic pulses are then received by the receiving transducer placed at the downstream flow.

Let the time taken by the ultrasonic pulses to travel from transmitter and received at the receiver is Δt. If the direction of propagation of the signal is same as the direction of flow then the transit time can be given by,

\[\Delta {{t}_{1}}=\frac{d}{{{V}_{s}}+{{V}_{f}}}\]

Where,

d = Distance between two crystals (i.e., transmitter and receiver).

V_s = Velocity of propagation of ultrasonic sound waves in the fluid.

V_f = Linear velocity of flow.

If the direction of the signal is opposite with the direction of flow then the transit time is given by,

\[\Delta {{t}_{2}}=\frac{d}{{{V}_{s}}+{{V}_{f}}}\]

The signal traveling in the same direction of flow is sinusoidal in nature having f Hz frequency has a phase shift of,

\[\Delta {{\phi }_{1}}=\frac{2\pi fd}{{{V}_{s}}+{{V}_{f}}}\text{ rad}\]

Similarly, the sinusoidal signal traveling in the opposite direction of flow has a phase shift of,

\[\Delta {{\phi }_{2}}=\frac{2\pi fd}{{{V}_{s}}-{{V}_{f}}}\]

Now the determination of transit time or phase shift gives the velocity of fluid flow. Using this ultrasonic flow meter the flow rate can be determined in two methods. One method involves the measurement of difference in transit time (Known as transit time difference method) and the other method involves the measurement of difference in frequency (Known as oscillating loop system).

The output of oscillator which is a sinusoidal signal of 100 kHz frequency is supplied to the transmitter which transmits these signals to the receiver. With the help of commutating switch the functions of both transmitter and receiver are reversed.

Therefore, the difference that exists in the transit time can be given by,

\[\Delta t=\Delta {{t}_{2}}-\Delta {{t}_{1}}\]

\[\Delta t=\frac{d}{{{V}_{s}}-{{V}_{f}}}-\frac{d}{{{V}_{s}}+{{V}_{f}}}\]

\[\Delta t=\frac{2dv}{V_{s}^{2}-V_{f}^{2}}\]

This difference in transit time can be determined using a phase sensitive detector, driven in synchronization with the commutator. Generally the flow velocity inside the pipe is very low and can be neglected. Therefore the difference in transit time becomes,

\[\Delta t\approx \frac{2dv}{V_{s}^{2}}\]

Thus, the Δt is linearly proportional to velocity of flow.

Another method of flow rate measurement using ultrasonic flow meter is shown in figure (2). This arrangement of flow rate measurement is based on frequency. It uses two self excited oscillating system in order to utilize the received pulses to trigger the transmitted pulses in feedback mechanism.

This helps to generate a train of pulses. The pulse repetition frequency for transmitter placed at upstream or in the forward propagating loop is given by,

\[{{f}_{1}}=\frac{1}{\Delta {{t}_{1}}}=\frac{1}{\frac{d}{({{V}_{s}}+{{V}_{f}}\cos \theta )}}=\frac{({{V}_{s}}+{{V}_{f}}\cos \theta )}{d}\]

Similarly, the pulse repetition frequency for transmitter placed at downstream or in the backward propagating loop is given by,

\[{{f}_{2}}=\frac{1}{\Delta {{t}_{2}}}=\frac{1}{\frac{d}{({{V}_{s}}-{{V}_{f}}\cos \theta )}}=\frac{({{V}_{s}}-{{V}_{f}}\cos \theta )}{d}\]

Therefore, the difference in these two frequencies is given by,

\[f={{f}_{1}}-{{f}_{2}}\]

\[f=\frac{({{V}_{s}}+{{V}_{f}}\cos \theta )}{d}-\frac{({{V}_{s}}-{{V}_{f}}\cos \theta )}{d}=\frac{2{{V}_{f}}\cos \theta }{d}\]

This frequency difference gives the flow rate of the fluid.

Advantages of Ultrasonic Flow Meter

1. Not required any obstruction to the flow.
2. It is not affected by changes in density, viscosity, and temperature.
3. The output is linearly proportional to the input.
4. Effectively used in bidirectional flow measurements.
5. High accuracy and also has an excellent dynamic response.

Disadvantages of Ultrasonic Flow Meter

1. The circuit arrangement is difficult.
2. The cost of the arrangement is high.

The post What is Ultrasonic Flow Meter? Working Principle, Diagram, Construction & Advantages appeared first on Electrical and Electronics Blog.

Working Principle of Electromagnetic Flow Meter

The measurement of flow rate using an electromagnetic flow meter depends on Faraday’s law of electromagnetic induction. When a pipe or tube carrying electrically conducting fluid is placed in a transverse magnetic field an e.m.f. will be induced across the electrodes connected to it. This voltage gives the measure of the velocity of the fluid or flow rate of the fluid.

Construction of Electromagnetic Flow Meter

An electromagnetic flow meter consists of a nonmagnetic and non-conducting pipe to carry the flow whose velocity or flow rate is to be determined (see Figure). To the opposite sides of this pipe a pair of insulated electrodes which are in contact with the fluid flow inside the pipe are connected. Now this pipe is placed between the two poles of an electromagnet or permanent magnet that produces magnetic field.

Working of Electromagnetic Flow Meter

When the conducting fluid whose flow rate is to be measured is made to flow through the pipe, it cuts the magnetic field causing some e.m.f. to be induced across the electrodes. This induced voltage is given by,

\[e=Blv\]

Where,

B — Flux density

l — Conductor length (this is equal to diameter of the pipe)

v — Velocity of the fluid (conductor)

From the above equation it is clear that the voltage induced across the electrodes is directly proportional to the diameter of pipe, average velocity of fluid and hence gives the volume flow rate of the fluid.

Advantages of Electromagnetic Flow Meter

1. This method does not cause any obstruction to the flow of fluid, hence pressure will not drop.
2. It can be used with pipes of any size.
3. Accuracy is good.
4. The relation between output voltage and flow rate is linear.
5. Effectively measures the flow rates of slurries, conducting fluids, sludge etc.
6. The output is independent of variations in temperature, viscosity, density and so on.

Disadvantages of Electromagnetic Flow Meter

1. Highly expensive.
2. The presence of gas and air bubbles in the fluid leads to errors.
3. The fluid under measurement must be conductive in nature.

Limitations of Electromagnetic Flow Meter

1. Its use is limited to conductive fluids only.
2. Its flow range is limited to 10^-3 g pm to 10⁴ g pm i.e., 0.5 to 4.95 × 10² m³/hr.

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