Question 2.Q.50: Find the current IL in the circuit shown in Fig. Q2.50.1 us......

Find the current I_L in the circuit shown in Fig. Q2.50.1 using Millman’s theorem.

2.50.1
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The circuit can be redrawn as shown in Fig. Q2.50.2 and then the parallel connected voltage sources can be converted into a single source as shown in Fig. Q2.50.3

{R}_{\mathrm{eq}}={\frac{1}{{\frac{1}{2}}+{\frac{1}{8}}}}=1.6~\Omega   ;  {E}_{\mathrm{eq}}=\left({\frac{12}{2}}+{\frac{0}{8}}\right)\times1.6=9.6V

{R}_{\mathrm{eq}2}=\frac{1}{\begin{array}{l}{{\frac{1}{2}}+{\frac{1}{3}}}\end{array}}=1.2\cdot\Omega    ;

{E}_{\mathrm{eq}}=\;\left({\frac{0}{2}}+{\frac{6}{3}}\right)\times1.2=2.4V

With reference to fig Q2.50.3,

\mathrm{{I_{L}}}={\frac{\mathrm{{E_{eq1}}}-\mathrm{{E_{eq2}}}}{{\mathrm{{R_{eq1}}}}+0.8+{\mathrm{{R}}}_{e q2}}}\,=\,{\frac{9.6-2.4}{1.6+0.8+1.2}}\,=\,2\,A
50.2.3

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