An AC supply with $=200ra\frac{d}{s}$ is used to power an RLC circuit. The total impedance of the circuit is $32\mathrm{.}0,$ and the total resistance $R=30\mathrm{.}0.$ Find a possible phase shift $$ between the current and the supply voltage at this frequency. Bonus if you give both possible values for $.(12$ pts$.)$

$=200ra\frac{d}{s},Z=32,R=30$

$\frac{O}{?}=ta{n}^{-1}(\frac{x_L-x_L}{R}),32=\sqrt[\phantom{2}]{40000+(x_L-x_C)}$

$ta{n}^{-1}(\frac{-38976}{32})-38976=(x_c-x_c),x_L=-38976+x_1$

$=(-89\mathrm{.}95or220\mathrm{.}05)$