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
STEP(1): calculation of load current in load
by using mesh analysis
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
