Transcript SUPERPOSITION - City University London

SUPERPOSITION
•
•
•
•
•
•
•
•
Superposition is a general principle that forms the
basis for a very powerful technique used to analyse
multisource circuits
Restricted to circuits with linear components like
resistors
Helps when determining the current through or voltage
across any component of a multisource circuit
Involves the computation of the current or voltage due
to each source acting alone
Therefore when we begin the computations, we
remove all sources except one
We make the contributions of the remaining sources
(either current source or voltage source) equal to zero
We replace ideal voltage sources by short circuits (V
= 0)
We replace ideal current sources by open circuits (I
= 0)
Superposition
1
PROCEDURE FOR ANALYSING A
CIRCUIT USING SUPERPOSITION
1.
2.
3.
4.
•
•
•
Select any one source in the circuit and remove all
others (by replacing them with short or open
circuits)
Compute the desired voltage or current in a
component when the only source present is the
one selected in step 1
Repeat steps 1 and 2, after selecting a new source
to be the only one present. Continue until the desired
voltage or current has been computed due to each
and every source acting alone
Add all the computed values obtained from analysing
the circuit with each source acting alone. The sum is
the actual voltage or current when all sources are
acting simultaneously (i.e. when all the sources are
present)
Important to take into account the polarities of the
quantities being added. E.g. One source produces a
current of 5A from left to right, and another 1A from
right to left. The total (net) current is 5+(-1)=4A from
left to right
Superposition can’t be used to find power dissipated
in a resistor, provided computation is carried out
after finding current through or voltage across!
Don’t add powers. Power is a nonlinear
mathematical operation
Superposition
2
SUPERPOSITION EXAMPLES (1)
•
Using the superposition principle
a) Find the current in the 15Ω resistor
b) Find the current in the 10Ω resistor.
10Ω
30V
30Ω
15Ω
Superposition
54V
3
SUPERPOSITION EXAMPLES (2)
•
Using the superposition principle, find the voltage
across the 1kΩ and the voltage across the 4kΩ resistor.
1kΩ
10mA
4kΩ
25V
Superposition
15V
3kΩ
4
SUPERPOSITION EXAMPLES (3)
•
•
To what voltage should the adjustable source E be set
in order to produce a current of 0.3A in the 400Ω
resistor.
If E is set to 30V, to what value should the current
source be changed in order that the total current in the
400Ω resistor be 0.3A?
200Ω
E
400Ω
Superposition
0.6A
5