$.$ A renewable energy research team is developing a sophisticated solar power in$-$

verter for remote mountain communities. The inverter must convert low$-$voltage

DC from solar panels into a stable AC signal for powering community facili$-$

ties. During prototype testing, they analyze a critical circuit designed to smooth

power output. The circuit is connected to a $5\mathrm{.}0$ kHz$,480$ V $($rms$)$ test source

with the following component specifications:

Inductor $($L$)$: $45\mathrm{.}0$ mH $-$ Helps stabilize current flow

Resistor $($R$)$: $6\mathrm{.}50$k$-$ Represents internal circuit losses

Capacitor $($C$)$: $4800$pF $-$ Helps filter and regulate voltage fluctuations

The engineering team needs to determine:

$1.$ The total circuit impedance

$2.$ The phase angle between voltage and current

$3.$ The RMS current in the circuit

$4.$ Average power dissipation

Your analysis will help optimize the inverter$$s performance for reliable electricity

in off$-$grid locations. How will the circuit behave under these conditions?