Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) PDF Download

Alternating Current Circuit

  • Alternating Current (A.C) – The current whose magnitude and direction both change with time and the same cycle is repeated after a regular interval of time is called alternating current. In India its frequency is 50 Hz and its magnitude at time t is called instantaneous value and is given by
  • I = I0 sin ωt 
  • where I0 = Peak value of current

 Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

As the variations are like sine curve, it is called sinusoidal A. C. Such type of A.C. is produced when a coil rotates in a uniform magnetic field with angular velocity ω. The flux associated with coil,
Ø = NBA cos ωt

where q = wt is the angle covered by normal to plane of coil with B-  in time t. Due to change in flux induced emf.
E = -df/dt = NBA w sinwt

E = Esin ωt and the corresponding current I = I0 sin ωt. 

  • Cycle – One complete set of positive and negative values of an alternating quantity is known as a cycle. A cycle may also sometimes be specified in terms of angular measure. In that case one complete cycle is said to spread over 360º or 2π radian.
  • Amplitude :- The maximum value, positive or negative of an alternating quantity is known as its amplitude
  •  Frequency (f):- The number of cycles/second is called the frequency of the alternating quantity.  Its unit is hertz (Hz). 
  • Time period (T) :- The time taken by an alternating quantity to complete the cycle is called its time period. Time period is the reciprocal of frequency.  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
  • Root mean Square (R. M. S) Value :- The r.m.s. value of an alternating current is given by that steady (D.C.) current which when flowing through a given circuit for a given time produces the same heat as produced by the alternating current when flowing through the same circuit for the same time.

R.M.S. value is the value which is taken for power purposes of any description.

 Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

  • Average or mean value :- The average value of an alternating current is expressed by that steady current which transfers across any circuit the same change as is transferred by that alternating current during the same time.

Eav = 0.636 Emax 

  • Form factor :- It is the ratio of R.M.S. value to the average value and denoted by Kf.

Form factor Kf  =  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
 Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Peak Value :- It is the ratio of max, value to R. M. S. Value or effective value. It is denoted by Kp.
Peak value Kp =  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

 

S.NO.Wave formForm factor KfPeak factor Kp
1.Sine wave –
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
R.M.S. value = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
Average value = 
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
2.

Half wave rectified sine wave

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

R.M.S. value = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
Average value = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
3.

Full wave rectified Sine wave –

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

R.M.S. value = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

average value = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
4.

Rectangular wave –

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

R.M.S. value = Imax Average Value = Imax

Kf = 1KP = 1
5.

Triangular wave –

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

R.M.S. value =  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Average value = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

 

Reasons for using alternating current (or voltage of sinusoidal form) –

(i) Mathematically it is quite simple.
(ii) Its integrals and differentials both are sinusoidal.
(iii) It tends itself to vector representation.
(iv) A complex wave form can be analysed into a series of sine waves of various frequencies and each such component can be dealt with separately.
(v) This wave form is desirable for power generation, transmission and utilisation. 

A.C. Through pure Ohmic resistance alone – Where a sinusoidal e.m.f. is placed across a pure resistance the current will be in phase with thee.m.f. and it shown graphically will be in phase with the e.m.f. curve.

 Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
The current I = V/R

A.C. Through pure capacitance alone – if a sinusoidal e.m.f. is placed across a capacitor the current will be

 Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

I = (2πf)CV

C = Capacitance in farads
f = frequency
V = Voltage (r.m.s. value)

XcAlternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

The expression  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)   is termed the capacitive reactance (XC) and the current is given by
 
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) . The power consumed is zero.

  • Phasor Algebra – The following are the methods of representing vector quantities.

(i) Symbolic notation
(ii) Trigonometrical form
(iii) Exponential form
(iv) Polar form

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(i) Symbolic notation E = a + jb

(ii) Trigonometrical form  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) (cosθ + jsinθ)

(iii) Exponential form E = [ Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)  general form]

(iv) Polar form    Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

  • A. C. series circuits (R – L C ircuit Resistance and Inductance in series) –

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

formulae – 

(1) Impedance Z =

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(where XL = 2π  f LW)

(2) Current  I = V/Z

(3) Power factor cosø = R/Z

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(4) Power consumed P = VI cosø

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

R.C. circuit (Resistance and capacitance in series) 

Formulae –

(1) Impedance  Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(where XcAlternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE))

 (2) Current I = V/Z

(3) Power factor cosø = R/Z

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(4) Power consumed = VI cosø( = I2P)

R-L-C circuit (Resistance, Inductance and capacitance in series)

 Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Formulae –

 (1) Impedance Z = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(2) Current = I = V/Z

(3) Power factor cos ø = R/Z

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

(4) Power consumed = VI cos ø (= I2 R)

A. C. Parallel Circuit – When two or more branches are connected in parallel, the circuit is said to be parallel circuit.
Properties of parallel circuit:
(1) The voltage across each branch is same
(2) The current in each branch is different and depends upon the value of impedance.
(3) The angle between voltage and current of each branch will be different.
(4) The total current will be the vector sum of branch currents.
(5) The total impedance will be

Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
(In A.C. series circuit Z = Z= Z+ Z3)

  •  Comparison of series and parallel resonant circuit –
S. No.AspectsSeries circuit (R-L-c)Parallel circuit R-L andC
1.Impedance at resonanceMinimumMaximum
2.Current at resonanceMaximum V/RMinimum
Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
3.Effective ImpedanceRL / CR
4.Power factor at resonanceUnityUnity
5.Resonant frequencyAlternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
6.It magnifiesVoltageCurrent
7.Magnification isAlternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
  • Three phase circuits – In case of three phase circuits, the three-phase currents are determined by considering each phase separately, and calculating the three-phase current from the phase voltage and impedances in the same manner as for single phase circuit. In practice three phase systems are usually symmetrical.

Having calculated the phase currents, the line currents are obtained from the following simple rule –

1. Star-connected system – Line current (IL) = phase current (Iph)

Line voltage (EL) = √3 phase voltage (= √3 Iph)

Line voltage (EL)= phase voltage (EPh)

2. Delta connected system

Line current (IL) = √3 phase current (= √3 Iph)

Line voltage (EL) = Phase voltage (Eph) 

Polyphase Circuits – More than one phase supply is called polyphase supply. If number of armature windings are used in the alternator, then this is called a polyphase alternator. The angle of displacement can be determined by the formula

Electrical displacement = Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Advantages of polyphase over single phase supply–
(i) The rating of a given machines increases with the increase in no. of phase. In case of three phase supply the rating of  3 phase motor will be nearly 1-5 times the output of single phase motor of same size.
(ii) For same ra ting the power factor of polyphase motor is higher than single phase motor
(iii) The efficiency of single phase motor is higher than polyphase motor.
(iv) In case of polyphase motors a revolving field is set up but in case of single phase motors there is no self starting.
(v) Polyphase system is more dependable than single phase system.
(vi) Parallel operation of 3 phase alternator is simple as compared to single phase alternator
(vii) The voltage regulation is less in polyphase system than single phase system
(viii) Polyphase motors are smooth in running than single phase motors.

Comparison between star and Delta connection
(i) In star connection similar ends are joined together where as in delta connection dissimilar ends are joined together.
(ii) In case of star connection, line voltage is √3 phase voltage whereas in case of delta connection line voltage is equal to phase voltage.

(iii) In case of star connection line current is equal to phase current whereas in delta connection line current is equal √3 phase current.
(iv) In case of star connection it is possible to carry the neutral wire to the load whereas in delta connection it is not possible.
(v) All distribution transformers are Delta/Star connected whereas power transformer are Delta/Delta connected.

Advantages and disadvantages of A.C. over D.C.
Advantage – 
(1) The generation of A.C. is found to be economical than that of D.C.
(2) The alternating voltage can be easily stepped up or stepped down by using a transformer.
(3) The alternating current can be regulated by using a choke coil without any significant wastage o electrical energy.
(4) The alternating voltage can be transmitted to distant places with only a very small loss in a.c. power.
(5) Further a.c. can be easily converted into d.c. by using rectifiers.

Disadvantages 
(1) The a.c. supply is mor e suidical and dangerous then d.c. in terms of shock received due to them.
(2) The alternating current always flows on the outer layer of the wire. It is called single thick wire used for d.c. the specially designed wire consisting of a number of thin wire is used.
(3) The alternating current can not be used in electrolytic processes such as electroplating, electrotyping etc.

The document Alternating Current Circuit | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Electrical Engineering SSC JE (Technical).
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FAQs on Alternating Current Circuit - Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

1. What is an alternating current circuit?
An alternating current (AC) circuit is a type of electrical circuit where the flow of electric charge periodically reverses direction. In an AC circuit, the voltage and current change sinusoidally over time. This is in contrast to a direct current (DC) circuit, where the flow of electric charge is constant and unidirectional.
2. How is alternating current produced in a circuit?
Alternating current is typically produced using a device called an alternator. An alternator consists of a rotating magnetic field and a stationary loop of wire. As the magnetic field rotates, it induces a changing magnetic flux through the wire loop, which in turn generates an alternating current. This current can then be used to power various electrical devices.
3. What are the advantages of using alternating current in circuits?
There are several advantages of using alternating current in circuits. Firstly, AC can be easily converted to different voltage levels using transformers, which allows for efficient transmission of electrical power over long distances. Secondly, AC circuits are more suitable for powering devices that require high power levels, such as motors and appliances. Additionally, AC circuits can be easily regulated and controlled using techniques like frequency modulation.
4. What are the differences between alternating current (AC) and direct current (DC) circuits?
AC and DC circuits differ in several ways. In an AC circuit, the voltage and current periodically change direction, while in a DC circuit, they are constant and unidirectional. AC circuits can be easily transformed to different voltage levels, while DC circuits require specialized converters. AC circuits are more suitable for long-distance power transmission, while DC circuits are commonly used in electronic devices. Finally, AC circuits can generate electromagnetic radiation, while DC circuits do not.
5. How does the frequency of an AC circuit affect its behavior?
The frequency of an AC circuit refers to the number of complete cycles that occur in one second. The behavior of an AC circuit is affected by its frequency in several ways. Firstly, the frequency determines the rate at which the voltage and current change direction, which can impact the performance of electrical devices. Secondly, the frequency affects the impedance of the circuit, which is a measure of its opposition to the flow of current. Finally, the frequency can also influence the efficiency of power transmission and the design of components like capacitors and inductors.
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