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Scholastic Video Book Series
Circuits & Systems
Book 1
By Professor Liyanage C De Silva, PhD
(with English Narrations)
scholastic-videos.com
(http://scholastic-videos.com/Scholastic-Book-SuperpositionTheorem-2014-11-30.pdf)
1
©Scholastic Tutors (Nov, 2014)ISVT 911-0-20-141130-1
SUPERPOSITIONTHEOREM
International Baccalaureate (IB)
2
Superposition Theorem
scholastic-videos.com
(CCT-001)
http://youtu.be/n8FT7TM0fOYClick here to see the video
• Question: Using the Superposition theorem find the voltage Vo of the circuit shown in the figure.
Superposition Theorem
scholastic-videos.com 3
• Superposition Theorem: Voltage across or current through an element is determined by summing voltage (or current) due to each independent source at a time.
• In order to perform this we need to eliminate all sources (except dependent sources) other than the one being considered.
• To eliminate a voltage source the terminals connected to the voltage source are short circuited.
• To eliminate a current source the terminals connected to the current source are open circuited.
Superposition Theorem
scholastic-videos.com 4
Superposition Theorem
• Solution: We need to determine the value of Vo with only one source at a time.
• There is a voltage source and a current source in this circuit.
• Hence we have to eliminate one at a time.
5http://youtu.be/n8FT7TM0fOYClick here to see the video
Superposition Theorem
scholastic-videos.com
• Step 1: Eliminate the current source by open circuiting.
• Let us assume the current in the circuit is equal to I1 as shown in the figure below.
• 𝐼1 =24𝑉
6+10+3 𝑘Ω= 1.263𝑚𝐴
• ∴ 𝑉𝑜1 = 1.263 3 𝑉 = 𝟑. 𝟕𝟖𝟗𝑽
6
Superposition Theorem
• Step 2: Now eliminate the voltage source by short circuiting.
• Let us assume the current in the left and right branches of the circuit are I2 and I3
respectively as shown in the figure.
7http://youtu.be/n8FT7TM0fOYClick here to see the video
Superposition Theorem
scholastic-videos.com
• 𝐼2 + 𝐼3 = 5𝑚𝐴
• 𝑉𝐴𝐵 = 𝐼2 × 6 = 𝐼3 × 10 + 3
• 𝐼2 = 5 − 𝐼3 𝑚𝐴
• 5 − 𝐼3 × 6 = 𝐼3 × 13
• 19𝐼3 = 30
• ∴ 𝐼3 =30
19= 1.579𝑚𝐴
• ∴ 𝑉𝑜2 = 1.579 3 𝑉 = 𝟒. 𝟕𝟑𝟕𝑽
• ∴ 𝑉𝑜 = 𝑉𝑜1 + 𝑉𝑜2 = 3.789 + 4.737 = 𝟖. 𝟓𝟐𝟔𝑽
𝑉𝑜1 = 1.263 3 𝑉 = 𝟑. 𝟕𝟖𝟗𝑽
A
B
8
http://youtu.be/n8FT7TM0fOYClick here to see the video
Superposition Theorem
• Verification of the result: Now let us consider both sources together.
• 𝐼′ + 𝐼′′ = 5𝑚𝐴
• 𝑉𝐴𝐵 = 24 + 𝐼′ × 6 = 𝐼′′ × 10 + 3
• 𝐼′ = 5 − 𝐼′′
• 24 + 5 − 𝐼′′ × 6 = 𝐼′′ × 13
• 19𝐼′′ = 54
• ∴ 𝐼′′ =54
19= 2.842𝑚𝐴
• ∴ 𝑉𝑜 = 3 × 𝐼′′ = 3 × 2.842𝑉 = 𝟖. 𝟓𝟐𝟔𝑽 Verified
𝑉𝑜 = 𝑉𝑜1 + 𝑉𝑜2 = 3.789 + 4.737 = 𝟖. 𝟓𝟐𝟔𝑽
A
B
9http://youtu.be/n8FT7TM0fOYClick here to see the video
Videos at: http://www.youtube.com/homevideotutor
10
(http://scholastic-videos.com/Scholastic-Book-SuperpositionTheorem-2014-11-30.pdf)
Scholastic Video Book Series
Circuits & Systems
Book 1
By Professor Liyanage C De Silva, PhD
http://liyanage-desilva.webs.com/
(with English Narrations)
©Scholastic Tutors (Nov, 2014)ISVT 911-0-20-141130-1
scholastic-videos.com
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