(Solved): Under assumption that input voltage Vi has the amplitude of \( 1 \mathrm{~V} \) calculate input cu ...

Under assumption that input voltage Vi has the amplitude of \( 1 \mathrm{~V} \) calculate input current I to the circuit presented in Figure 1 assuming \( \mathrm{R}=1 \mathrm{k} \Omega \) and \( \mathrm{C}=10 \mu \mathrm{F} \). Using equations below obtain an amplitude ratio of the voltages \( \mathrm{Vi} / \mathrm{V} 0 \) and a phase shift \( \Theta \) between them at \( 50 \mathrm{~Hz} \) and \( 5 \mathrm{MHz} \). What theoretically you can conclude about RC circuit? \[ \begin{array}{l} \frac{V_{o}}{V_{i}}=\frac{1 / j \omega C}{R+1 / j \omega C}=\frac{1}{1+j \omega R C}=\frac{1}{\sqrt{1+(\omega R C)^{2}}} \angle-\tan ^{-1}(\omega R C) \\ V_{o} \text { Laggs } V_{\mathrm{i}} \text { by } \theta=\tan ^{-1}(\omega R C) \end{array} \] Under assumption that input voltage Vi has the amplitude of \( 1 \mathrm{~V} \) calculate input current I to the circuit presented in Figure 2 assuming \( \mathrm{R}=1 \mathrm{k} \Omega \) and \( \mathrm{C}=10 \mu \mathrm{F} \). Using equations below obtain the amplitude ratio of the voltages \( \mathrm{Vi} / \mathrm{V} 0 \) and the phase shift \( \Theta \) between them at \( 50 \mathrm{~Hz} \) and \( 5 \mathrm{MHz} \). What theoretically you can conclude about CR circuit? \[ \begin{array}{l} \frac{V_{o}}{V_{i}}=\frac{R}{R+j X_{c}}=\frac{R}{\sqrt{R^{2}+X_{c}^{2}}} \angle \tan ^{-1}\left|\frac{X_{C}}{R}\right|, \quad X_{C}=-1 / \omega C \\ V_{o} \text { Leads } V_{\mathrm{i}} \text { by } \theta=\tan ^{-1}\left|\frac{X_{C}}{R}\right| \\ \text { Phase of } V_{\mathrm{i}} \text { has been changed by } \theta=\tan ^{-1}\left|\frac{X_{C}}{R}\right| \end{array} \]