Sum

Find current I_{X} using Superposition theorem

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#### Solution

(1) 36V is active other all are inactive.

10Ω || 5Ω = 3.33Ω

Applying KCL to the circuit.

−36π+5πΌ_{π}+3.33πΌ_{π}=0

8.33πΌ_{π}=36

πΌ_{π}=4.321Am

(2) 12V is active other all are inactive.

Applying KVL at mesh 1

−5πΌ_{1}+10(πΌ_{1}−πΌ_{2})=0

−5πΌ_{1}+10πΌ_{1}−10πΌ_{2}=0 ……..(1)

Applying KVL at mesh 2

12−5πΌ_{2}−10(πΌ_{2}−πΌ_{1})=0

12=−10πΌ_{1}+15πΌ_{2} ………..(2)

From (1) and (2) we get,

πΌ_{1}=2.142π΄ and πΌ_{2}=1.0714π΄

πΌ_{π}(2)=2.142 Am

(3) 6A is active and other all are inactive.

10Ω || 5Ω = 3.33Ω

πΌ_{π}(3)=6 x `3.33/(3.33+5)`= 2.398 Am

πΌ_{π}(3)=−2.398 Am

πΌ_{π}= −2.398+2.142+4.32=4.065

π°_{πΏ}=π.πππ Am

Concept: Superposition Theorem

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