# Question Please show complete solution FEEDBACK AND CONTROL SYSTEMS TRANSFER FUNCTION OF ELECTRICAL SYSTEMS 3. Given the circuit below, solve for $$\mathrm{G}_{2}(\mathrm{~s})=\frac{V_{L}(s)}{V(s)}$$ $$\mathrm{Gs}=\frac{V_{L 3}(s)}{V_{I N}(s)}$$

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Transcribed Image Text: FEEDBACK AND CONTROL SYSTEMS TRANSFER FUNCTION OF ELECTRICAL SYSTEMS 3. Given the circuit below, solve for $$\mathrm{G}_{2}(\mathrm{~s})=\frac{V_{L}(s)}{V(s)}$$ $$\mathrm{Gs}=\frac{V_{L 3}(s)}{V_{I N}(s)}$$
Transcribed Image Text: FEEDBACK AND CONTROL SYSTEMS TRANSFER FUNCTION OF ELECTRICAL SYSTEMS 3. Given the circuit below, solve for $$\mathrm{G}_{2}(\mathrm{~s})=\frac{V_{L}(s)}{V(s)}$$ $$\mathrm{Gs}=\frac{V_{L 3}(s)}{V_{I N}(s)}$$
&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/2Solution Given the AC Circuit to find the transfer function So the inductive reactance in the s-domain will be \begin{align*} \mathrm{{X}_{{L}}} &= \mathrm{{s}{L}={s}}\\[3pt]\mathrm{{Z}_{{2}}} &= \mathrm{\frac{{{1}{\left({1}+{s}\right)}}}{{{1}+{1}+{s}}}=\frac{{{1}+{s}}}{{{2}+{s}}}} \end{align*}Explanation:Please refer to solution in this step.Step2/2So by the Voltage dividing rule the VL will be \( \begin{align*} \mathrm{{V}_{{L}}{\left({s}\right)}} &= \mathrm{\frac{{Z}_{{2}}}{{{Z}_{{2}}+{s}}}×\frac{{s}}{{{1}+{s}}}×{V}{\left({s}\right)}}\\[3pt]\mathrm{\fr ... See the full answer