Question

Find current I_X using Superposition theorem

Answer 1

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

10Ω || 5Ω = 3.33Ω
Applying KCL to the circuit.
−36𝑉+5𝐼_𝑋+3.33𝐼_𝑋=0
8.33𝐼_𝑋=36
𝐼_𝑋=4.321Am

(2) 12V is active other all are inactive.
Applying KVL at mesh 1
−5𝐼₁+10(𝐼₁−𝐼₂)=0
−5𝐼₁+10𝐼₁−10𝐼₂=0 ……..(1)
Applying KVL at mesh 2
12−5𝐼₂−10(𝐼₂−𝐼₁)=0

12=−10𝐼₁+15𝐼₂ ………..(2)
From (1) and (2) we get,
𝐼₁=2.142𝐴 and 𝐼₂=1.0714𝐴
𝐼_𝑋(2)=2.142 Am

(3) 6A is active and other all are inactive.
10Ω || 5Ω = 3.33Ω

𝐼_𝑋(3)=6 x `3.33/(3.33+5)`= 2.398 Am

𝐼_𝑋(3)=−2.398 Am

𝐼_𝑋= −2.398+2.142+4.32=4.065

𝑰_𝑿=𝟒.𝟎𝟔𝟓 Am