(Solved):   A sinusoidal voltage \( \Delta v=42.5 \sin (100 t) \), where \( \Delta v \) is in volts an ...

 

A sinusoidal voltage \( \Delta v=42.5 \sin (100 t) \), where \( \Delta v \) is in volts and \( t \) is in seconds, is applied to a series \( R L C \) circuit with \( L=150 \mathrm{mH}, C=99.0 \mu \mathrm{F} \), and \( R=52.0 \Omega \). (a) What is the impedance (in \( \Omega \) ) of the circuit? \( \Omega \) (b) What is the maximum current (in \( A \) )? A (c) Determine the numerical value for \( \omega \) (in \( \mathrm{rad} / \mathrm{s} \) ) in the equation \( i=I_{\max } \sin (\omega t-\varphi) \). \( \mathrm{rad} / \mathrm{s} \) (d) Determine the numerical value for \( \varphi \) (in rad) in the equation \( i=I_{\max } \sin (\omega t-\varphi) \). \( \mathrm{rad} \)