# Thevenin theorem in Electrical Network

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THEVENIN THEOREM  :

This theorem state that any two terminal network containing voltage source and current source , can be replaced by an equivalent circuit consisting of an voltage source Vth in series with an impedance Rth,

Where Vth is an open circuited voltage between terminals of network and Rth is impedance calculated between terminal of network

Electrical Network ( N1)

by help of thevenin theorem ,above electrical network N1 can be represented as

where Rth = thevenin impedance

Vth = thevenin voltage

Thevenin equivalent circuit of above network

PROOF OF THEVENIN THEOREM :

In above circuit , first  calculate current  in impedance  by using mesh analysis and after that calculate current  in impedance  by using thevenin theorem , if these current will be same ()  then thevenin theorem will be proved

for Mesh1 ( contains Z1,Z2 and E ) : suppose in mesh1 current flow is I1

for Mesh2 ( contains Z2,Z3 and ) suppose in mesh2 current flow is I2

Apply KVL in Mesh1:

E= Z1I1 +Z2(I1-I2)

E= (Z1+Z2)I1 -Z2I2

here I2 =  ( current flow in load )

E= (Z1+Z2)I1 – Z2                                     eq(1)

Apply  KVL in Mesh2:

Z3I2+I2 +Z2 (I2 – I1) =0

I2=

(Z3++Z2) – Z2I1  =0                            eq(2)

After solving eq(1) and eq(2) ,will get

= EZ2/( Z1Z3+Z1+Z1Z2+Z2Z3+Z2)       eq(3)

STEP(2): calculation of load current ( ) in load  by using Thevenin theorem

(1) Calculation for Vth: remove the load  and find the voltage across open circuited terminals as shown in figure below

Voltage across open circuited terminal will be

Vth   = EZ2 / ( Z1+Z2)

(2) Calculation for Rth : for calculation of Rth first make voltage source E short circuited and calculate equivalent resistance  across open circuited terminal as figure shown below

Rth  =    Z3 + Z1Z2 / (Z1+Z2)

(3) Calculation of current  in  :  in thevenin equivalent circuit as shown below

=   Vth / ( Rth +

after calculation

= EZ2 /( Z1Z3+Z1+Z1Z2+Z2Z3+Z2)     eq(4)

from eq(3) and eq(4) it is clear that

=    hence thevenin theorem proved