A $30-$V AC source has a an angular frequency $=250ra\frac{d}{s}$ and is connected into an RLC series circuit as shown.

a$.$ Determine $v,v_R,v_L,$ and $v_c$ at a time $t=20ms?$

b$.$ Is the sum of $v_R,v_L,$ and $v_c$ greater than, less than, or equal to $v?$

c$.$ Determine V$,V_R,V_L,$ and $V_c.$

d$.$ Is the sum of $V_R,V_L,$ and $V_c$ greater than, less than, or equal to V $?$

e$.$ Explain why your answer to parts B and D makes sense.