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)

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©Scholastic Tutors (Nov, 2014)ISVT 911-0-20-141130-1

SUPERPOSITIONTHEOREM

International Baccalaureate (IB)

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Superposition Theorem

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(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

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• 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

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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

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• 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

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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

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• 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

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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

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(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