##### Q3

Q3.Resistance of wire is ‘r’ohm.The wire is stretched to double of it’s length and then it’s resistance in ohm is?
ANS:
Given:-
Resistance of a wire is ‘r’ ohms.

It’s length is doubled.

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To find:- New resistance of wire that is RnewSolution:-
Let r1 be the radius of wire.

Let the new length of wire be = l1R= ?laa= ?r2? ?r12l=?rnew2lnew? ?rnew2=?r12l2l=?r122? Rnew=?.lnewanew=?2l?r22=4?l?r12=4?la=4r’ohms’
Q.4 Draw (or bring out) the comparison between a star connected and a delta three phase system.Write the necessary mathematical expressions relevant diagrams in support of your answers.

SOLUTION:-

STAR CONNECTION DELTA CONNECTION
In star connection,the starting or finishing ends of three coils are connected together to form the neutral point. 1.In delta connection,the opposite ends of three coils are connected together.

Star connection is used where we require neutral terminal to obtain phase voltage. 2.Delta connection is used where we not require neutral terminal to obtain phase voltage
In star connection,the line current is equal to the phase current. 3.In delta connection the line current is equal to the root three times of the phase current.

In star connection,line voltage equal to root three times of the phase voltage. 4.In delta connection line voltage is equal to the phase voltage.

In star connection,each winding receives 230 volts. 5.In delta connection,each winding receives 415 volts.

Star Connection in a 3 Phase System
In the Star Connection, the similar ends of the three windings are connected to a common point called star or neutral point. The three line conductors run from the remaining three free terminals called line conductors.

The finish terminals a2, b2, and c2 of the three windings are connected to form a star or neutral point. The three conductors named as R, Y and B run from the remaining three free terminals as shown in the above figure.

The current flowing through each phase is called Phase current Iph, and the current flowing through each line conductor is called Line Current IL. Similarly, the voltage across each phase is called Phase Voltage Eph, and the voltage across two line conductors is known as the Line Voltage EL.

Relation Between Phase Voltage and Line Voltage in Star Connection

Phasor Diagram

The arrowheads on the emfs and current indicate direction and not their actual direction at any instant.

Circuit GlobeCircuit TheoryStar Connection in a 3 Phase System
Star Connection in a 3 Phase System
In the Star Connection, the similar ends (either start or finish) of the three windings are connected to a common point called star or neutral point. The three line conductors run from the remaining three free terminals called line conductors.

The wires are carried to the external circuit, giving three phase, three wire star connected systems. However, sometimes a fourth wire is carried from the star point to the external circuit, called neutral wire, forming three phase, four wire star connected systems.

Contents:
Relation Between Phase Voltage and Line Voltage in Star ConnectionRelation Between Phase Voltage and Line Voltage in Star ConnectionThe star connection is shown in the diagram below.

Considering the above figure, the finish terminals a2, b2, and c2 of the three windings are connected to form a star or neutral point. The three conductors named as R, Y and B run from the remaining three free terminals as shown in the above figure.

The current flowing through each phase is called Phase current Iph, and the current flowing through each line conductor is called Line Current IL. Similarly, the voltage across each phase is called Phase Voltage Eph, and the voltage across two line conductors is known as the Line Voltage EL.Relation Between Phase Voltage and Line Voltage in Star Connection
The Star connection is shown in the figure below.

As the system is balanced, a balanced system means that in all the three phases, i.e., R, Y and B, the equal amount of current flows through them. Therefore, the three voltages ENR, ENY and ENB are equal in magnitude but displaced from one another by 120 degrees electrical.

The Phasor Diagram of Star Connection is shown below.

The arrowheads on the emfs and current indicate direction and not their actual direction at any instant.

Now,

There are two phase voltages between any two lines.

Tracing the loop NRYN

To find the vector sum of ENY and –ENR, we have to reverse the vector ENR and add it with ENY as shown in the phasor diagram above.

Therefore,

Similarly,

Hence, in Star Connections Line voltage is root 3 times of phase voltage.

Relation Between Phase Current and Line Current in Star Connection
The same current flows through phase winding as well as in the line conductor as it is connected in series with the phase winding.

Where the phase current will be

The line current will be

Hence, in a 3 Phase system of Star Connections, the Line Current is equal to Phase Current.

Delta Connection In a 3 Phase System
In Delta (?) or Mesh connection, the finished terminal of one winding is connected to start terminal of the other phase and so on which gives a closed circuit. The three line conductors are run from the three junctions of the mesh called Line Conductors.

The current flowing through each phase is called Phase Current (Iph), and the current flowing through each line conductor is called Line Current (IL).

The voltage across each phase is called Phase Voltage (Eph), and the voltage across two line conductors is called Line Voltage (EL).Relation Between Phase Voltage and Line Voltage in Delta Connection

Similarly,

Where, the phase voltages are

The line voltages are

Hence, in Delta Connection Line Voltage is equal to Phase Voltage.

phasor diagram

As we know, IR = IL, therefore,

Similarly,

Hence, in Delta connection line current is root three times of phase current.

Q2.Draw an electrical circuit and in it label for all possible nodes,branches and loops.

NODE N=BRANCH B=
LOOP L=

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