For the circuit of Fig. 2.64, determine the relationship between [latex]\nu[/latex] and [latex]i[/latex].

It is seen that we can find [latex]\nu_{2}[/latex] by applying KCL at node 2 [latex] \begin{aligned} & \frac{\nu_{2}}{20}+\frac{\nu_{2}-\nu}{10}+\frac{\nu_{2}-10}{10}=0 & (\text{i}) \\ &\left(\frac{1}{20}+\frac{1}{10}+\frac{1}{10}\right) \nu_{2}=\left(\frac{1}{10}\right) \nu+1 \\ & 0.25 \nu_{2}=0.1 \nu+1 \\ & \nu_{2}=0.4 \nu+4 & (\text{ii})\end{aligned} [/latex] Now applying KCL at node 3 [latex] \begin{gathered} \nu_{3}=\nu \\ \frac{\nu-\nu_{2}}{10}+\frac{\nu-10}{20}-i=0 \\ 0.15 \nu-0.1 \nu_{2}-1-i=0 \end{gathered} [/latex] Substituting for [latex]\nu_{2}[/latex] [latex] \begin{array}{r} 0.15 \nu-0.1(0.4 \nu+4)-1-i=0 \\ 0.19 \nu-0.4-1-i=0 \end{array} [/latex] or [latex]\nu=5.26 i+3.16 ; \text { required relationship }[/latex]

Question 2.ASP.35: For the circuit of Fig. 2.64, determine the relationship bet...

Basic Electrical Engineering

For the circuit of Fig. 2.64, determine the relationship between $\nu$ and $i$ .

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