Electrical Engineering

Waveform:      A shape formed by plotting instantaneous values of voltage or current as ordinate (y-axis) against time as abscissa(x-axis) is called waveform.  Instantaneous Value:     The value of alternating quantity at any instant is called instantaneous value.E.g., in above graph v=0 at t=0. Cycle:      One complete set of positive and negative values of an alternating quantity. — 1 cycle = 360 ° or 2 Π   Cycle is shown as below. Alternation: Half cycle is called one alternation. 1 alternation =180 ° or Π .  Alternation is shown as below. Time Period:      Time required to complete one cycle is called time period.It is represented by T.  Frequency:       The literal meaning of frequency is repetition.In alternating quantity terminology it is defined as         " Number of times alternating voltage or current cycles  are formed on graph in one second is called  frequency."   The unit of frequency is cy

Star Delta Transformation: There are some networks in which resistors are neither in series nor in parallel. Such networks are star-connected or delta-connected resistors.A familiar case is a three terminal network e.g delta network or star network.It is not possible to simplify such networks by employing series or parallel technique.In order to solve them we transfer them into one another and then apply series parallel techniques. We can transfer star-connected into delta-connected resistances by keeping the two networks electrically equivalent and vice versa. By electrically equivalent   networks means    “ Resistance between any two terminals of one network is equal to the resistance between the corresponding the second network.” Delta to star transformation: Resistance between terminals A and B (Δ-connected) R AB =R AB ||(R BC +R CA ) R AB =R AB (R BC +R CA )/R AB +R BC +R CA Resistance between terminals A and B (Star-connected) R AB =R A +R B As two networks

Combinations of resistors: Resistors are arranged in one of three forms to form electrical networks according to our desired demand. 1.Series Network   2. Parallel Network  3.Star or Delta Network                                        Series Network: A network of resistors where there is only one path for current to flow is called a series resistive circuit. It means the current in a series circuit remains the same but voltage divides across the resistors. Total resistance of the circuit is more than any resistor connected in series. A series network is shown in the following figure. Total resistance  of a series connected resistors is found by the formula R t  =R 1 +R 2 +R 3 +……….+R n I = E/R t Total voltage = E E = IR 1 +IR 2 +IR 3 +……..+IR n The equivalent circuit after calculating total resistance is given by                            Parallel Network: Such a circuit in which resistors are arranged in a way that current has multiple pa

Conductance: The conductance of a material is its property which tells us with   how easily current can flow through that material. In simplest way it is defined as “Reciprocal of resistance is called conductance.” It is denoted by G and is given by                     G=1/R Unit: The unit of conductance is mho or siemen and is represented  Ʊ. Relation: As conductance is reciprocal of resistance so it is inversely proportional to the length of the conductor but directly proportional to the area. According to above statement                G  α 1/L  ........(1)                G  α A ...........(2) By combing above two relations we have              G α A/L or                   G=   σ A/L where    σ= Conductivity and is defined as Conductivity: The reciprocal of resistivity is called conductivity. It is represented by σ. Unit: The unit of conductivity is mho per meter( Ʊ/m ) or siemen per meter.   Alternatively             

Temperature: When electric current passes through a conductor the temperature of the conductor increases due to collision of electrons with other electrons and with atoms and molecules of conductor. This temperature has a great effect on the resistance of the conductor and to find this effect a term is coined called temperature coefficient of resistance.   Temperature coefficient of resistance: Temperature coefficient of resistance tells us about the effect of temperature on the resistance of a material.It is given by the following equation                                     α = (Rt-Ro)/Rot                            where   α =temperature coefficient  Rt=resistance at temperature=t in centigrade  Ro=  resistance at temperature=0 in centigrade Unit: The unit of temperature coefficient of resistance is per centigrade. Effect of temperature on the resistance of electrical materials: Electrical materials are also classified into two major types on the basis

As conductor is made up of some material that will have certain dimensions such as length and area etc that plays a part in calculating the resistance. The resistance of a conductor depends on the following parameters 1:Length of conductor 2:Cross-sectional area of conductor 3:Resistivity  4:Temperature of the conductor Now we will explain all of above four parameters one by one . Length and Area of conductor : The resistance of material is directly proportional to the length of the conductor but inversely proportional to the area of the conductor. We know that when length of a material increases its area will decrease which means path or channel through which electrons flow will decrease. Under such a condition more collision will occur resulting in increase of resistance.Mathematically,                                                                                                  RαL .......(1)                                         Rα1/A ........(2)  By combining above