Question 2.16: Applying KCL, determine current IS in the electric circuit t......

Applying KCL, determine current I_S in the electric circuit to make V_0 = 16 V in the network shown in Fig. 2.40.

figure 2.40
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Now applying Kirchhoff’s current law to nodes A and B we have

I_1=I_2+I_s               (i)

and                I_2+I_3=\frac{V_1}{4}            (ii)

also voltage of node B = V_0 =16 V
Voltage across AC + voltage across AB = voltage at node B.

\begin{gathered} V_1+4 I_2=16 \mathrm{~V}\quad (iii) \\ I_1=\frac{V_1}{6}\quad(iv) \end{gathered}

Solving eq (i), (ii), (iii), and (iv) we have

\mathrm{V}_1=12 \mathrm{~V} \quad \mathrm{I}_1=2 \mathrm{~A} \quad \mathrm{I}_2=1 \mathrm{~A} \quad \mathrm{I}_{\mathrm{S}}=\mathrm{I}_1-\mathrm{I}_2=2-1=1 \mathrm{~A}

Therefore,                           I_{\mathrm{s}}=1 \mathrm{~A} \quad I_3=\frac{V_1}{4}-I_2=3-1=2 \mathrm{~A}

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