Thevenin theorem and Norton theorem

1. Harsha Singh Bais
Assistant Professor Department of
Physics and Electronics
Shri Shankaracharya Mahavidyalaya,
Bhilai
1Network Theorem

2.  Introduction
 Thevenin Theorem
 Norton Theorem
2Network Theorem

3. Network analysis is the process of finding the voltages across, and the
currents through, all network components. There are many techniques
for calculating these values
Definitions
 Component A device with two or more terminals into which, or out of
which, current may flow
 Node A point at which terminals of more than two components are
joined. A conductor with a substantially zero resistance is considered to
be a node for the purpose of analysis. Branch The component(s) joining
two nodes.
 Mesh A group of branches within a network joined so as to form a
complete loop such that there is no other loop inside it .
 Port Two terminals where the current into one is identical to the current
out of the other.
 Circuit A current from one terminal of a generator, through load
component(s) and back into the other terminal. An electrical circuit is a
path in which electrons from a voltage or current source flow
Network Theorem 3

4.  A linear network consisting of a number of voltage
sources and resistances can be replaced by an
equivalent network having a single voltage source
called Thevenin’s voltage (Vth ) and a single
resistance called Thevenin’s resistance ( Rth)
 Thevenin voltage is obtained at the terminal with
open circuit
 Thevenin resistance is obtained by replacing all the
voltage sources by a short circuit.
 Thevenin voltage and Thevenin resistance are
connected in series with the load resistance
 Total load current is calculated by
Network Theorem
4

5. Network Theorem
5
Consider a network or a circuit as shown. Let E be the emf of the cell
having its internal resistance r = 0 and RL load resistance across AB .
To find Vth :
• The load resistance RL is removed
and the circuit is opened. The current I
in the circuit will be according to the
Kirchoff second law for closed loop
then I=E/R1+R2
• The voltage across AB = Thevenin’s
voltage Vth.
•The voltage across AB will be equal to
voltage at R2
Vth=IR2 then Vth=ER2 / R1+R2

6. Network Theorem 6
To find Rth :
The load resistance RL is removed. The cell is
disconnected and the wires are short as
shown.
The effective resistance across AB = Thevenin’s resistance Rth .
[ R1 is parallel to R2 and this combination in series with R3 ]

7. Network Theorem 7
Thus, to find the load current IL ,Vth and Rth are
connected in series
This proves the Thevenin Theorem

8.  A linear active network consisting of the independent
or dependent voltage source and current sources and
the various circuit elements can be substituted by an
equivalent circuit consisting of a current source in
parallel with a resistance.
 The current source being the short-circuited current
across the load terminal and the resistance being the
internal resistance of the source network.
 Norton’s theorem is the converse of Thevenin’s
Theorem
Network Theorem 8

9. Network Theorem
9
Step 1 – Remove the load resistance of the circuit.
Step 2 – Find the internal resistance Rint of the source
network by deactivating the constant sources.

10. Network Theorem 10
Step 3 – Short the load terminals and find the short
circuit current ISC flowing through the shorted load
terminals using conventional network analysis
methods.

11. Network Theorem 11
Step 4 – Norton’s equivalent circuit is drawn by
keeping the internal resistance Rint in parallel
with the short circuit current ISCand find the
current through it known as load current IL.
• IL is the load current
• Isc is the short circuit current
• Rint is the internal resistance of the circuit
• RL is the load resistance of the circuit
This is all about Norton’s Theorem.

12. Network Theorem
12
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