$9\mathrm{.}30$ The circuit in Fig. P$9\mathrm{.}30$ is operating in the sinusoidal steady state. Find $i_o(t)$ if $v_s(t)=25sin2000tV.$

Finum Do an

$9\mathrm{.}40$ a$)$ The source voltage in the circuit in Fig. P$9\mathrm{.}40$ is $v_g=200cos500tV.$ Find the values of $L$ such that $i_g$ is in phase with $v_g$ when the circuit is operating in the steady state.

b$)$ For the values of $L$ found in $($a$),$ find the steadystate expressions for $i_g.$

Figure P$9\mathrm{.}40$

$9\mathrm{.}43$ The sinusoidal voltage source in the circuit in Fig. P$9\mathrm{.}43$ is developing a voltage equal to $50sin400tV.$

a$)$ Find the Th$$venin voltage with respect to the terminals a$,$b$.$

b$)$ Find the Th$$venin impedance with respect to the terminals a$,$b$.$

c$)$ Draw the Th$$venin equivalent.

Solve all the questions $9\mathrm{.}30,9\mathrm{.}40,$ and $9\mathrm{.}43$ with all the steps knowing that the answer to P$9\mathrm{.}30$ is io$($t$)=1\mathrm{.}55$cos$(2000$t$-124\mathrm{.}82)$ A and P$9\mathrm{.}40$ L$1=8$H and L$2=2$H and p$9\mathrm{.}43$ vth$=-20-$j$10$ v