$10\mathrm{.}9$ Find the average power dissipated in the $30$ resistor in the circuit seen in Fig. P$10\mathrm{.}9$ if $i_g=6cos20,000tA.$

$10\mathrm{.}18$ a$)$ Find the average power, the reactive power, and the apparent power supplied by the voltage source in the circuit in Fig. P$10\mathrm{.}18$ if $v_g=40cos{10}^{6}tV.$

b$)$ Check your answer in $($a$)$ by showing $P_{\text{d}\text{e}\text{v}}=P_{\frac{?}{abs}}.$

c$)$ Check your answer in $($a$)$ by showing $Q_{\text{d}\text{e}\text{v}}=Q_{\frac{?}{abs}}.$

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$10\mathrm{.}33$ The steady$-$state voltage drop between the load and the sending end of the line seen in Fig. P$10\mathrm{.}33$ is excessive. A capacitor is placed in parallel with the $150$ kVA load and is adjusted until the steady$-$state voltage at the sending end of the line has the same magnitude as the voltage at the load end, that is$,4800$ V $($rms$).$ The $150$ kVA load is operating at a power factor of $0\mathrm{.}8$ lag. Calculate the size of the capacitor in microfarads if the circuit is operating at $60$ Hz $.$ In selecting the capacitor, keep in mind the need to keep the power loss in the line at a reasonable level. Please show all the steps For $10\mathrm{.}9$ know that p$30$ohm$=600$W and for P$10\mathrm{.}18$ Sh$=-6\mathrm{.}4-$j$4\mathrm{.}8$ VA and for P$10\mathrm{.}33$ C$=44\mathrm{.}43$ microfarad