(Solved): For each of the first-order ficter circuits shown in I-IV: (a) determine the corner frequency \( \ ...

For each of the first-order ficter circuits shown in I-IV: (a) determine the corner frequency \( \omega_{c} \) (b) determine the filter type (lowpass, highpass) and give reasoning. (c) based on your conclusion in part(b), determine \( H_{0} \) if lowpass or \( H_{\infty} \) if highpass. recalling that the standard forms are \[ \begin{array}{l} H(s)=H_{0} \frac{1}{1+s / \omega_{c}}=H_{0} \frac{\omega_{c}}{s+\omega_{c}} \text { (lowpass) } \\ H(s)=H_{\infty} \frac{s / \omega_{c}}{1+s / \omega_{c}}=H_{\infty} \frac{s}{s+\omega_{c}} \text { (highpass) } \end{array} \]