$5.1(10+2 \mathrm{pts})$ Refer to the circuit powered by a 120 $\mathrm{V}$ rms, $60-\mathrm{Hz}$ voltage source as shown below. (a) (2 pts) Determine the power factor of the circuit load in (A). (b) (2 pts) Determine the average power dissipation in (A). (c) (6 pts) What is the capacitor's value that will give a power factor of 0.96 lagging when connected in parallel to the load as shown in (B)? (d) (extra 2 pts) What is the capacitor's value that will give a power factor of 0.96 leading when connected in parallel to the load as shown in (B)? (A) (B)

please for 5.1 only solve part d).

5.2 (20 pts) In the following circuit, the voltage source $\nabla_{s}=100 \angle 0^{\circ} \mathrm{V} \mathrm{rms}, 60 \mathrm{~Hz}$ supplies power to three load circuits with impedances $Z_{1}, Z_{2}$, and $Z_{3}$. The following information was deduced from measurements performed on the three load circuits: Load $Z_{1}: 50 \mathrm{~W}$ at $\mathrm{pf}=0.9$ lagging Load $Z_{2}: 80$ VA at pf $=0.75$ leading Load $Z_{3}: 100$ vA at $p f=0.6$ lagging (a) (6 pts) Are $Z_{1}, Z_{2}$, and $Z_{3}$ inductive or capacitive circuits? (b) (8 pts) Determine the total complex power (in rectangular form) dissipated by the parallel combination.

$5.3(20+6 p t s)$ (a) (2 pts) Obtain the transfer function $H(\omega)=$ $V_{o}(\omega) / V_{i}(\omega)$ of the circuit below in terms of $\mathrm{R}_{1}, \mathrm{R}_{2}$ and $\mathrm{C}$. (b) (4 pts) Convert the transfer function $H(\omega)$ obtained from (a) into the form \[ H(\omega)=\frac{j \omega / \omega_{1}}{1+j \omega / \omega_{2}} \] and present $\omega_{1}$ and $\omega_{2}$ in terms of $R_{1}, R_{2}$ and $C$. (c) (4 pts) Continue (b) and find the expressions of magnitude $|H(\omega)|$ and phase $\angle H(\omega)$ in terms of $\omega_{1}$ and $\omega_{2}$. (d) (8 pts) If $R_{1}=8 \mathrm{k \Omega}, R_{2}=2 \mathrm{k \Omega}$, and $C=1 \mu \mathrm{F}$, determine the values of magnitude $|H(\omega)|$ and phase $\angle H(\omega)$ at low frequency $(\omega \rightarrow 0)$ and at high frequency $(\omega \rightarrow \infty)$. \begin{tabular}{|c|c|c|} \hline$\omega$ & $|H(\omega)|$ & $\angle H(\omega)$ \\ \hline$\omega \rightarrow 0$ & & \\ \hline$\omega_{c}$ & & $45^{\circ}$ \\ \hline$\omega \rightarrow \infty$ & & \\ \hline \end{tabular} (e) (2 pts) is this circuit a high-pass or a low-pass filter? (f) (extra 6 pts) Determine $\omega_{c}$ at which $\angle H\left(\omega_{c}\right)=45^{\circ}$. Determine $\left|H\left(\omega_{c}\right)\right|$ and show that \[ \frac{\left|H\left(\omega_{c}\right)\right|}{|H(\omega \rightarrow \infty)|}=\frac{1}{\sqrt{2}} \]

please for 5.3 solve e and f only.