Network theorem part 1

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

 Introduction
 Thevenin Theorem
 Norton Theorem
2Network Theorem

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

 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

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

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 ]

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

 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

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.

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.

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.

Network theorem part 1

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Network theorem part 1