$\text { Find the current } I_ x \text { using superposition theorem. } $

Solution:

Selecting 30 Amp source

KVL to loop

$ \begin{aligned} \\ 20-5 I_x^{\prime}-1 I x-4 I_x^{\prime} &=0\\ \\ -10 I_x^{\prime} &=-20 \\\\ I_x^{\prime} &=2 \text { Amp }....(1) \\ \end{aligned} \\ $

Selecting 30 Amp source

KVL to outer-100p

$ \begin{gathered} \\ -5 I_x^{11}-1\left(I_x^{11}-30\right)-4 I_x^{\prime \prime}=0 \\\\ -10 I_x^{\prime \prime}=-30 \\ \end{gathered} \\ $

$ I_x^{\prime \prime}=3...(2)\\ $ Amp

According to superposition theorem

$ \begin{aligned} \\ I_x &=I_x+I_x 1 \\\\ &=2+3 \\\\ I_x &=5 \mathrm{Amp}\\ \end{aligned}\\ $