Posts Tagged ‘Circuit’

First of all let us introduce with some common elements of a circuit. It is a most common problem that an Electrical Engineer can understand these facts, but could not able to give proper definition of these. So, let see how to define them properly.

Figure 1: An electric network showing nodes, branches, elements and loops.

Electric Network A connection of various circuit elements can be termed as an electric network. The circuit diagram shown in Figure 1 is an electric network.

Electric Circuit A connection of various circuit elements of an electric network forming a closed path is called an electric circuit. The closed path is commonly termed as either loop or mesh. In Figure 1, meshes BDEB, ABCA and BCDB are electric circuits because they form a closed path. In general, all circuits are networks but not all networks are circuits.

Node A connection point of several circuit elements is termed as a node. For instance, A, B, C, D and E are five nodes in the electric network of Figure 1. Please note that there is no element connected between nodes A and C and therefore can be regarded as a single node.

Branch The path in an electric network between two nodes is called a branch. AB, BE, BD, BC, CD and DE are six branches in the network of Figure 1.

Now, come to the analytical part of circuit. There are three primary laws of solving a DC circuit: Ohm’s Law, Kirchoff’s Voltage Law (KVL) and Kirchoff’s Current Law (KCL). We all already have much better knowledge about Ohm’s Law, which is “V = IR”. It does not mean that we don’t know about KVL and KCL. Obviously we do, but I just want to re-install these in your mind with definitions and applications.

Kirchoff’s Voltage Law (KVL):

“The sum of all the voltages (rises and drops) around a closed loop is equal to zero”

In other words, the algebraic sum of all voltage rises is equal to the algebraic sum of all the voltage drops around a closed loop. In figure 1, consider mesh BEDB, then according to KVL, V3 = V4 + V5

Example: In each of the circuit diagram in Figure 2, write the mesh equations using KVL.

Figure 2: Circuit diagrams to demonstrate the application of KVL in the above example.

Figure 2(a) contains a single loop hence a single current, is flowing around it. Therefore a single equation will result as given below,

Vs = IR1+IR2  ……………………………………………………………… (1.1)

If Vs, R1, R2 are known, then I can be found.

Figure 2(b) contains two meshes with currents I1 and I2 hence there will be two equations as shown below. Note that the branch containing R2 is common to both meshes with currents I1 and I2 flowing in opposite directions.

Left Loop:       Vs = I1R1+(I1I2)R2

Vs = (R1+R2)I1R2I2     ……………………………. (1.2)

Right Loop:     0 = (I2I1)R2+I2R3

0 = –R2I1+(R2+R3)I2         …………………………..…. (1.3)

Given Vs, R1, R2 and R3, equations 1.2 and 1.2 can be solved simultaneously to evaluate I1 and I2.

For the figure 2(c), three equations need to be written as follows. Also note that there is no circuit element shared between loops 2 & 3 hence I2 and I3 are independent of each other.

Left Bottom Loop:   Vs = (I1-I3)R1+(I1-I2)R2
Vs = (R1+R2)I1-R2I2-R1I3       
…………………. (1.4)

Right Bottom Loop:    0 = (I2-I1)R2+I2R3
0 = -R2I1+(R2+R3)I2           
………………….. (1.5)

Upper Loop:     0 = (I3-I1)R1+I3R4
0 = -R1I1+(R1+R4)I3                     ..
….……………… (1.6)

If Vs and resistors’ values are known, the mesh currents can be evaluated by solving equations 1.4, 1.5 and 1.6 simultaneously.

Resistors in Series: Consider figure 3 with one voltage source and two resistors connected in series to form a single mesh with current I.

According to KVL, Vs = V1+V2

Using Ohm’s Law (V = IR),

IReq = IR1+IR2

Req = R1+R2        ………………………… (1.7)

Where, Req = combined or equivalent resistance of the series network. In general, for n number of serial resistors, Req is given by,

Req = R1+R2+R3+….+Rn           ………………………………….. (1.8)

Voltage Divider Rule (VDR): VDR provides a useful formula to determine the voltage across any resistor when two or more resistors are connected in series with a voltage source. In figure 3, the voltage across the individual resistors can be given in terms of the supply voltage and the magnitude of individual resistances as follows,

…………………………….. (1.9)

………………………………… (1.10)

In general, for n number of resistors connected in series, the voltage across the i th resistor can be specified as,

…………………………….. (1.11)

This is everything till now. Next, I’ll discuss about KCL and more circuit analysis methods.

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There are basic two varieties of open circuit breakers:

  1. DeadTank – compartment of circuit breaker, which is in earth potential.
  2. LiveTank – compartment of circuit breaker, which is in line potential.

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SF6 Circuit Breaker

The structure of circuit breaker controls the techniques in which, the circuit breaker is putted up. This can be one of following ways.

1. Earth Mounting and Base Mounting: the major advantages of this sort of mounting are – ease, ease of formation, ease of protection and removal of support arrangements. An additional benefit is that in internal substations, there is lessening in the tallness of the structure. A weakness however is also and that to avoid risk to workers, the circuit breaker is enclosed by an earthed barricade, which raises the area requisite.

2. Retractable Breakers: these types of circuit breakers have the benefit of being gap saving owing to the actuality that isolators may be putted up in the same region of authorization that has to be permitted between the retractable circuit breaker as well as the live permanent links. Another benefit is that there is the simplicity and protection of preservation. Moreover such a mounting is inexpensive since at least two insulators for each phase are still desired to support the permanent circuit breaker plug links.

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3. Suspended Breakers: at superior voltages tension insulators are more inexpensive than post or base insulators. Through this kind of mounting the live tank circuit breaker is balanced by tension insulators from transparency arrangements, and detained in a steady position by comparable insulators tensioned to the earth. There is the maintained benefit of cheap costs as well as simplified basics, and the arrangements used to hang up the circuit breakers can be used for additional functions.