Brief definition and measurement of voltage

In electrical circuit voltage play important role, it is act as an energy source caused current to flow. In other word voltage is pressure from an electrical circuits pushes the charged electrons through a conducting loop to enabling the charge to do work such as illuminating a light hear conducting loop means close circuits of conducting wire .The unit of voltage is volt denoted as (V) we can also called electromotive force (EMF), denoted as (E).The value of EMF is E=B L V sinӨ 10^-8 volts when conductor moves close circuit in magnetic field, where E-EMF,B-flux density, V-velocity of conductor  cm/sec, L-length of conductor. Voltage can be AC (alternating current) and DC (direct current).AC voltage pulsating nature in both directions and DC voltage constant nature in one direction only. AC voltage is either single phase or three phases. According to utility AC voltage categorize below;

·         Low tension (LT) voltage either single phase (110 Volts, 240 Volts) or three phases (440 Volts) up to 1000 volts used for domestic purpose.

·         M V (medium voltage) is three phases from 6.6 kilo volt to 33 kilo volt generally used for industrial purpose.

·         HT (High tension) voltage is three phases from 66 kilo volt to 132 kilo volt is transmission voltage.

·         E H T (Extra High tension) voltage is three phases from 220 kilo volt and above is also transmission voltage.

The DC voltage gets it from cell, battery or by converting AC voltage to DC voltage using converter. The DC voltages categorize below; 1.5 Volt from dry cell torch, 5 Volt cell phones other electronics circuits.12, 24 48 volt DC etc in auto mobile vehicles. In traction system locomotive converting ac voltages to dc voltage using converter 600 volt,12 kilo volt,15 kV,30 kV and 40 kV DC utilize by locomotive.

We can check the presence of voltage in a circuit by using test lamp, neon glow lamp tester and high voltage tester etc. In test lamp method two test lead of insulated wire one is against under test conductor other against ground when lamp glow between conductor and ground than the voltage is present. Neon glow lamp tester completes the circuit human body capacitance to earth and glow up. High voltage tester to check the presence of high voltage without touching the conductor can be detected by holding a tester in close proximity to the conductor.

Voltmeter is an instrument used to measured potential difference between two points in electrical circuits. Voltmeter is always connected to parallel with the circuits because its internal resistance is high if it is connected to series fault in readings because minimize the current in circuit due to presence of high resistance will change the potential difference. Usually analog and digital voltmeter used.

ANALOG VOLTMETER

                Analog voltmeter is MI (moving iron), MC (moving coil) and electrostatic type. Further we categorize moving iron voltmeter is  attraction, repulsion, induction and dynamo types and moving coil voltmeter is permanent magnet and dynamo types. In moving iron voltmeter consists of movable soft iron piece and other is fixed coil. The interaction of flux produce by these two elements produced deflecting torque pointer attached to the soft iron piece. In moving coil voltmeter the coil is movable which is wounded on soft piece placed in permanent magnet. When current start flowing through this coil rotates about its own axis in vertical position pointer connected in it. Electrostatic type voltmeter based on electrostatic principle in such type meter two charged plate one is fixed and other is movable repulsion between these two plate caused developed deflecting torque. Such type of meter high sensitive and used for high voltage measurements. Dynamo meter type voltmeter consists of a pair of coil that is fixed and other movable coil interaction between two coil produce a deflecting torque. Such types of meters used for DC voltage measurements.

DC analog meter

AC analog meter

DIGITAL METER

Clamp meter and multi meter given in image below  such type of meter convert analog to digital converter and show the readings in digital display ,used for low voltage measurements  three phase and single phase up to 1000 volts.In both the image shows the single phase AC voltage. We can also measure the DC voltages through these meters.Both have two test lead black and red used for measurement.

Clamp meter

Multi meter

HT VOLTMETER

We can not connect the voltmeter directly in high tension (HT) lines,potential transformer use to step down the voltage and this PT voltage given to analog or digital voltmeter for measuring HT voltage.In this image digital voltmeter with selector used for measuring HT (11kv) voltage. In selector switch 110 volts comes from 11kv over head line step down by PT (11KV/110Volts) and 220 volts aux. supply given to voltmeter.PT connected to parallel of the HT line and used for step down the HT voltage. 

HT digital voltmeter with selector switch

 The PT primary winding has large number of turn and secondary winding much small number of turns co-axial winding is used for reduced the leakage reactance. This is also called instrument transformer. 

               

               

   

Concept of AC Three Phase Generation.

    3 phase AC Sinusoidal 

In single phase AC circuit one rectangular coil placed in uniform magnetic field but in case of three phases AC circuit three rectangular coils placed in uniform magnetic field an angle of 120 degree phase difference each other rotate with uniform angular velocity ω rad/sec.  rotates such that R- phase wave form started at 0 degree, Y-phase 120 degree and B-phase 240 degree displaced each other’s shown in figure below.In three phase the value of emf induced in the phases  Red(R), Yellow(Y) and Blue(B)

R is E_R =V_M sin ωt,

Y is E_Y = V_M sin (ωt-120 degree) and

B is E_B= V_M sin (ωt-240 degree) = V_M sin (ωt+240 degree)

   3 phases waveform

We can say the phase Y lags 120 degree and B 240 degree lags behind to the R phase. The sums of three phases induced emfs is zero i.e. E_R +E_Y +E_B =0. First the R phase reached the maximum than Y-phase after that B-phase we can say the phase sequences is R-Y-B shown in figure below;Two type of balance supply and load arrangement in three phase circuit one is the star connection and another delta connection. The circuit will be balance when the value of voltage and current is equal magnitude.  Three phase AC system mainly used in industrial applications. When the value of in each phase voltage RY, YB and BR are in equal magnitude displaced 120 degree each other the supply is balanced. In case of balance load in three phase circuit the value of Impedance (Z) is equal magnitude in each phase i.e. RY, YB and BR.

Star connected load:

Star connected balance load

In star connected balanced load shown in above figure E_R, E_Y and E_B is the voltage in R, Y and B phase is phase voltage and E_RY,E_YB and E_BR is voltage between two lines RY,YB and BR called line voltage. The line current I_R,I_Y and I_B flow in each line which is equal to the phase current. According to Kirchhoff’s voltage law the value of the relation between phase voltage and line voltage is

E_RY= E_R- E_Y

E_YB = E_Y- E_B

E_BR= E_B - E_R,Where E_R, E_Y and E_B phase voltages and  E_RY,E_YB and E_BR  line voltages. Also, in case of star connection balance load the value of quantities given below:

E_l= √3 E_ph     

I_l= Iph

P=3 E_ph I_ph cosφ

P=√3 E_l I_l cosφ ,Where E_ph- phase voltage, E_l- line voltage, I_ph- phase current, I_l- line current, cosφ power factor.

Delta connected load:

Delta connected balance load

In delta connected balanced load shown in figure I_R, I_Y and I_B is the line current in R, Y and B phases and I_RY, I_YB and I_BR is phase current. In delta connected load phase voltage is equal to the line voltage.  According to Kirchhoff’s current law the value of the relation between phase current and line current is

I_R= I_RY -I_BR

I_Y = I_YB -I_RY

I_B = I_BR -I_YB,Where I_R, I_Y and I_B is the line current. Also, in case of delta connection balance load the value of quantities given below:

I_l= √3 I_ph     

E_l= Eph
P=3 E_ph I_ph cosφ

P=√3 E_l I_l cosφ,Where E_ph- phase voltage, E_l- line voltage, I_ph- phase current, I_l- line current, cosφ power factor.

Mathematical summery AC single phase

1. E=E_m sin ωt            Sinusoidal EMF
2. I= I_m sin ωt             Sinusoidal current
3. ω =2πf                     Angular frequency
4. I_av=2I_m/π                Average value of sinusoidal current
5. I_rms= I_m/√2             RMS value of sinusoidal current
6. FF= I_rms/ I_av              Form factor
7. PF= I_m/ I_rms               Peak factor
8. P=VI cosφ               Active power (Watt)
9. Q=VI sineφ             Reactive power (VAR)
10. S= √ P²+Q²            Apparent power (VA)
11. Cosφ=R/Z               Angle between resistance and impedance

Mathematical summery AC three phase

1. E_R =V_M sin ωt                            Sinusoidal EMF R phase
2. E_Y = V_M sin (ωt-120 degree)     Sinusoidal EMF Y phase  
3. E_B = V_M sin (ωt+240 degree)    Sinusoidal EMF B phase
4. P=3 E_ph I_ph cosφ                         Power three times the single phase

Differences between AC single phase and three phase

1. Flow of power in AC single phase through single conductor and three phase through three conductors.
2. The voltage in single phase is 230Volt and three phase 440 Volt measured through voltmeter.
3. Single phase supply mostly used in domestic appliances and three phase supply used in industrial heavy load.
4. The single phase power loss more, efficiency less compare to three phases. 
5. AC single phase power transmission less economical compare to three phases.
6. AC single phase known single phase 2-wire system but  AC three phase known as 3-phase 4-wire system.  

Concept of AC single phase circuits.

AC CIRCUIT

                 AC voltage applied to a circuit call AC circuits. The Flow of electrons in AC circuits is bidirectional.AC circuits depends on load connected in it are four types. 1. Load as a resistance(R) 2.Load as a capacitive(C) 3. Load as an inductive (L) 4. Load as a (R-L-C)

1. Load as a resistance(R): 

Restive single phase AC circuit 

In ac circuit load is a resistance, the voltage and current are in same phase shown in figure below i.e. maximum value of voltage is reached at the same instant as peak current. In Phasor diagram the angle between voltage (V) and current (I) is zero.

(A)   v=Vm sin ωt value of alternating voltage.

(B)   i= Im sin ωt where Im= Vm/R value of alternating current.

(C)   P= Vm Im/2*(1-cos2ωt) Instantaneous power.

(D)  P= Vm/2 * Im/2 Average power.

2.Load as a capacitive(C): 

Capacitive single phase AC circuit

 In ac circuit which has only a capacitor is a device stored the charge the phase difference between voltage and current is 90 degree i.e. current lead the voltage by 90 degree in this image the peak value of voltage at 90 degree before the current reached the maximum in zero degree. In Phasor diagram the angle between voltage (V) and current (I) is 90 degree i.e. current leads the voltage by 90 degree.

(A) v=Vm sin ωt ,value of alternating voltage.

(B)  i= Im sin (ωt+ 90 degree), where Im=ωC Vm, value of alternating current.

(C)  P= Vm Im/2 *sin2ωt, Instantaneous power.

(D)  P= 0, Average power.

3. Load as a Inductive (L): 

Inductive AC single phase circuit 

If AC circuit purely inductive (a coil of wire wound on ferromagnetic material)  the phase difference between voltage and current again 90 degree but current legging 90 degree behind the voltage i.e. voltage reached the maximum or peak 90degree after the current reach the peak. In Phasor diagram the angle between voltage (V) and current (I) is 90 degree i.e. current lags the voltage by 90 degree.

(A)   v=Vm sin ωt ,value of alternating voltage.

(B)   i= Im sin(ωt- 90 degree),where Im= Vm/ωL,value of alternating current.

(C)   P= - (Vm Im/2* sin2ωt),Instantaneous power.

(D)   P= 0, Average power.

4. Load as a Restive, capacitive and inductive (R-L-C): 

R-L-C single phase circuit

Such type of circuit called RLC circuit. The overall resistance of the RLC circuit is known as impedance (Z). In this phasor diagram resistance along the X- axis and Inductive reactance (XL), Inductive capacitance (XC) along y –axis   90 degree phase difference to the resistance. Between Inductive reactance (XL) and Inductive capacitance (XC) phase difference is 180 degree opposite each other. The value of impedance Z is √(R^2 )+(XL-XC)^2 according to ohms law V=IZ. When (XL)> (Xc) the circuit is inductive, (XL) < (Xc) the circuit is capacitive (XL) = (Xc) the circuit is purely resistive.

Behavior and properties of DC circuit.

Power sources basically two types AC and DC discussed previously .If we applied DC voltage in a circuit called DC circuit.

DC CIRCUIT

                               DC circuit is three types 1. Series 2. Parallel 3. Combination of series and parallel.

1. In a series circuit flow of electrons moved to one path towards battery positive terminal to negative terminal. In figure 9 V DC voltage source applied flow of electrons 1-2-3-4 through all the resistances. In a Series the equivalent value of resistance R=R1+R2+R3 i.e. Total value of resistances(R)=3+10+5= 18 kohm. According to ohms law the value of current in this circuit I=V/R means I=9/18=0.5 Amps. The value of voltage different at different resistance at R1 voltage is V1= IxR1=0.5 X 3 =1.5 V DC similarly at R2 5 V DC and R3 2.5 V DC.We can say in series circuit the voltage is different at different resistance but sum is equal to source voltage.

DC series circuit

• Total voltage=v1+v2+v3...Voltage different at different resistance.
• Total current= I1=I2=I3…Current same through the circuit.
• Total Resistance=R1+R2+R3...Resistance added.
• Total Capacitance= 1/c1+1/c2+1/c3...When capacitor connected in series DC circuit.
•  Total Inductance = L1+L2+L3...When inductance connected in series DC circuit.
• Voltage Diversion V1=I*R1,V2=I*R2 ...and so on
• Current Diversion I1=V1/R1,I2=V2/R2...are same.

 I    2.In parallel circuit the flow of electrons is different in different branches. In this figure below there are three resistancesR1,R2 and R3 arrangement in parallel branches 2-7,3-6 and 4-5 the flow current is different in every branch but the value of voltage is same in throughout the circuit i.e. 9 VDC. The value of total resistance in the circuit 1/R=1/R1+1/R2+1/R3 means R=R1*R2*R3/R1+R2+R3 in this circuit R=10*2*1/10+2+1=20/13, R= 1.54kohm. Total current I(R1)=V/R1,9/10=0.9 A(branch 2-7) similarly I(R2)=4.5 A,( branch 3-6) I(R3)=9 A( branch 4-5)i.e.  I(T)=I(R1)+I (R2)+ I(R3)=14.4 A. 

DC Parallel circuit

• voltage=v1=v2=v3...Voltage same through the same circuit.
• Total current= I1+I2+I3…Current is the sum of all branches.
• Total Resistance=1/R1+1/R2+1/R3…Division of Resistance added.
• Total Capacitance= c1+c2+c3…When capacitor connected in parallel DC circuit.
• Total Inductance =1/ L1+1/L2+1/L3 ...When inductance connected in series DC circuit.
•  Voltage Diversion V1=Total voltage *R1/(R1+R2+R3)…and so on
• Current Diversion I1=Total current*(R2+R3+..)/(R1+R2+R3+… are same. 

 3. In Combination series parallel circuit resistances are connected in the combination of series and parallel shown in below image R1,R2and R3, R4 in parallel means R(12)= R1*R2/R1+R2 and R(34)=R3*R4/R3+R4areinseriesR(12)=100*250/100+250=71.4ohms,R(34)=350*200/350+200=127.27 ohms. Here R (12) and R (34) in series i.e. total value of in this circuit R (Total) = R (12) + R (34) =198.67 ohms. Then the Value of current is 24/198.67=0.12A and voltages at are different at R (12), R (34) we can calculate as similarly to series circuit.

combination of series and parallel

DC circuit rules:

1. I=V/R (Ohms law)

2. P=V.I=sqr.of  IR= sqr.of V/R (Joule law)

3. ƩVi=0 at a current loop sum of voltage drop is Zero (Kirchhoff’s voltage law).

4. ƩIi=0 at a node sum of currents values is Zero (Kirchhoff’s current law).

5. C=Q/V value of capacitance= charge /voltage.

6. Energy stored in capacitor = C*sqr.of V/2

7. Energy stored in inductor = L* sqr. of I/2

Generation of AC Single Phase Sinusoidal.

(A) GENERATION OF AC SINGLE PHASE SINUSOIDAL VOLTAGE

                                                                AC circuits widely used in domestic and industrial applications, When applied voltage is alternating nature means the flow of electrons forward and reverse both the direction. In DC circuit only resistance will oppose the flow of electrons but in AC circuit resistance, capacitance and inductance oppose the flow of electrons. Firstly we talk about generating of alternating sinusoidal voltage single phase three phases discussed later. In this image any rectangular coil having turn (N) kept in uniform magnetic field (B) and the coil rotating anticlockwise at uniform angular velocity ω red/sec at vertical position (A) flux φ linking the coil is zero because it is parallel to the magnetic field at this position angle is 0 degree between the magnetic field and the coil.   

Rectangular coil in
magnetic field B

When the coil starts moves anticlockwise direction some angle increase the flux linking hence the EMF (voltage) induced in figure (B). In figure (C) the coil moved from 0 to 90 degree at this position flux linking maximum because the line of magnetic field and the coil perpendicular to each other maximum value EMF and linking flux φ max .Again the coil moved from 90 to 180 degree flux linking reduced figure (D) at 180 degree flux φ linking the coil is zero because it is parallel to the magnetic field at this electrons completed half cycle. Next the same cycle flow of electrons reverses from 180 to 270 degree maximum flux linking  but negative value but the coil achieved 270 to 360 value of flux linking zero and completed a cycle.  

(B) ALTERNATING QUANTITY SINUSOIDAL WAVE FORM

AC sinusoidal wave form 

The amplitude alternating EMF varies at w.r.t. time means at point A less than at point B they are instantaneous value. The maximum value (+Em) attends by EMF at 90 degree called a peak or maximum value. Time period (T) is the time taken in second to complete one cycle. The number of cycle completed in one second called frequency measured in (Hz)

In this figure maximum flux 𝚽 in downward direction at any angle θ the flux divided in two component   𝚽m sin⍵t along with the coil and 𝚽m cos⍵t perpendicular to coil mention in image. Along a the coil flux not induced  perpendicular component 𝚽m cos⍵t EMF induced in the coil .when no of turn in the coil is N then value of EMF is

e= -N *d𝚽 / dt (rate of change of flux wrt time)

the value of  𝚽 = 𝚽m cos⍵t 

e= -N *d𝚽 / dt 

Kept value of  𝚽  in above equation become

e= -N *d  / dt *( 𝚽m cos⍵t)

e=N*𝚽m ⍵sin⍵t(after differentiating)

e=Em sin⍵t where Em= N*𝚽m*⍵ induced emf and induced current is i=Im sin⍵t the are the induced emf and current in sinusoidal  AC wave.