26409484 Circuit Theory

8/8/2019 26409484 Circuit Theory

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Circuit Theory

1. Basic Circuit

2. Circuit Network With LoadResistance

3. Circuit Analysis/Electrical Network

4. Circuit With Inductor(L)

5. Circuit With Capacitor(C)

6. Circuit With Reactance(X) andImpedance(Z)



1. Basic Theory

1. Draw the Basic Circuit

2. Unit and Term-

1. Ampere (A)-electrical current

2. Volt (V)-different potential.

3. Ohm(Ω)-resistance

4. Coulomb (Q)-electrical charge

5. E.m.f.- Electromotive force

3. Part of Basic Circuit (next page)

Figure 3: BasicCircuit

At least 4 part:1.Source of emf

2.Conductor3.A load4.Switch (control)



Symbol Symbol

Resistor

Variable Resistor Lamp

Cell Watt meter

Inductor Amp meter

Capacitor Volt meter

VV

AA

ww

Wire no

connected

Wire

connected

Node / Junction



2. Circuit Network With LoadResistance(R)

• Connection of resistors1. Series-

• R total=R1+R2+Rn

• I total=I (R1) = I (R2) = I (Rn)

• E=V(R1) + V (R2) +V(Rn)• Voltage drop depend on resistor value

1. Parallel-• 1/R total=1/R1+1/R2+1/Rn

• I total=I (R1) + I (R2) + I (Rn)

• E=V(R1) = V (R2) = V(Rn)



3. Circuit Analysis/ElectricalNetwork

1. Ohm’s law

2. Kirchhoff’s Current Laws (KCL)

3. Kirchhoff’s Voltage Laws (KVL)

4. Thevenin’s Theorem

5. Maximum Power Transfer

6. Wye-Delta Transformations



1. Ohms Law (1)

• Ohm’s law states that the voltage acrossa resistor is directly proportional to thecurrent I flowing through the resistor.

• Mathematical expression for Ohm’s Lawis as follows:

iRv =



V

I R

VI R

V

I R

Example



Nodes, Branches and Loops

• A branch represents a single elementsuch as a voltage source or aresistor.

• A node is the point of connectionbetween two or more branches.

• A loop is any closed path in a circuit.



Nodes, Branches and Loops

Example

How many branches, nodes and loops are there?

Original circuit

Equivalent circuit



3. Kirchhoff’s Current Laws (KCL)

•states that :

–the algebraic sum of currents entering a node is zero. or

– The total currents enter a node=The current exit a node

0

1

=∑=

N

n

ni

Mathematically,

itotal =i1+i3+i4=i5+i2…

….(ii)

itotal =i1+i3+i2+i4+i5=

0…(i)



Example: Give theexpression of itotal

itotal =i1=i2+i3…….(ii)

itotal =i1-i3+i2=0…(i)Answer:



4. Kirchhoff’s Voltage Law (KVL)

• states that: – the algebraic sum of all voltages around a closed path

(or loop) is zero.

Mathematically,

054321 =−+−−vvvvv



4. Kirchhoff’s Voltage Law

(KVL)Example

• Applying the KVL equation for the circuit of thefigure below.

v a-v 1-v b-v 2-v 3 = 0

V 1 = IR1 v 2 = IR2 v 3 = IR3

⇒

v a-v b = I(R1 + R2 + R3 )

321 R R R

vv I

ba

++−

=



5. Thevenin’s Theorem

It states that a linear two-terminalcircuit (Fig. a) can be replaced by anequivalent circuit (Fig. b) consisting of a voltage source V

TH in series with a

resistor RTH

,

where

• VTH is the open-circuit voltage at the

terminals.

• RTH is the input or equivalent resistance atthe terminals when the independentsources are turned off.





Step of Thevenin’s Theorem

• Step 1:

– Remove resistor(RL) and mark terminal a-b

• Step 2:

–

Find R TH

by close voltage supply and open currentsupply

• Step 3:

– Find V Th at terminal a-b

•

Step 4: – Draw equivalent circuit for Thevenin and put RL



6. Maximum Power Transfer

L

Th

TH L

R

V P R R

4

2

max =⇒=

If the entire circuit is replaced byits Thevenin equivalent except forthe load, the power delivered tothe load is:

The power transfer profile withdifferent RL

For maximum power dissipated

in RL, Pmax , for a given R TH ,and V TH ,

L

LTh

Th

LR

R R

V Ri P

22

+==



7. Wye-Delta Transformations

)(1

cba

cb

R R R

R R R

++=

)(2

cba

ac

R R R

R R

R ++=

)(3

cba

ba

R R R

R R R

++=

1

133221

R

R R R R R R R

a

++=

2

133221

R

R R R R R R

Rb

++=

3

133221

R

R R R R R R R

c

++=

Delta -> Star Star -> Delta

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26409484 Circuit Theory