Wednesday 27 February 2013
Superposition theorem
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Superposition theorem
The Superposition theorem states that if a linear system is driven by more
than one independent power source, the total response is the sum of the
individual responses.
If the network contains more than one voltage or current source, superposition allows for a solution to be found by considering each voltage or current source separately and then adding the results. To consider each source separately, all other voltage sources are open circuited and all other current sources are short circuited.
If the network contains more than one voltage or current source, superposition allows for a solution to be found by considering each voltage or current source separately and then adding the results. To consider each source separately, all other voltage sources are open circuited and all other current sources are short circuited.
EXAMPLE
Find Vx
Solution
Consider 4V source
From the above circuit
resistors 2Ω and 5Ω are in parallel
Resultant resistance is =
( 2 * 5 ) / (2 + 5) = 10 / 7
Replacing the resultant
resistance in the given circuit
Adding 3Ω and 10/7 Ω we
get 31/7 Ω
Applying voltage divider
rule Vx = V * ( R1/ (R1 + R2 ) we get
Vx = 4 * ( 7 / 38 ) = 28/38 = 0.7368 V
Vx = 0.7368 V
Now considering 5V source
Rearranging the above
circuit
Applying nodal analysis at
node A
Assume node voltage be Va
Va + Va + Va
– 5 = 0
4 5 2
4 5 2
Solving above equation we
get Va = (50 / 19 ) V
Applying voltage division
rule
Voltage across 1 Ω
resistance = 0.6578 V
If we compare above
circuit with given circuit the polarities are opposite to each other.So reverse the sign of
voltage across 1 Ω
Therefore Voltage across 1
Ω resistance Vx = ─ 0.6578 V
Now consider 2A current source
From the above circuit 2 Ω
and 5 Ω are in parallel
So resultant resistance =
(10 / 7) Ω
(10 / 7) Ω and 1Ω are in
series then the resultant circuit = ( 17
/ 7 ) Ω
Applying current division
rule
Current through desired
resistance = (current * opposite resistance ) total resistance
Current through ( 17 / 7 )
Ω resistance = 1.105 A
If we expand ( 17 / 7 ) Ω resistance,
we get
Vx = 1* 1.105 = 1.105 V
Vx = 1.105 V
Therefore by superposition theorem voltage across 1
Ω resistance is
Vx = 0.7368 ─ 0.6578
V + 1.105
Vx = 1.184 V
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4 Responses to “Superposition theorem”
26 October 2014 at 15:31
sorry but i think you mean all voltage sources should be replaced by short cicuit and all current sources should be replaced by an open circuit.
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24 May 2020 at 23:06
You wrote the wrong statement on superposition. In that all independent voltage sources are short circuited and current sources are open circuited instead you wrote it in opposite manner. Thank you.
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