Voltage and current for a circuit with two elements in series are expressed as follows:

$\mathrm{v}\left(\mathrm{t}\right)=170\sin (6280\mathrm{t}+\mathrm{\pi }/3)\text{ volts }\mathrm{i}\left(\mathrm{t}\right)=8.5\sin (6280\mathrm{t}+\mathrm{\pi }/2)\text{ amperes }$

What are the values of the elements?

$\begin{array}{l}\cos \mathrm{\varphi }=\cos \left(\frac{\mathrm{\pi }}{2}-\frac{\mathrm{\pi }}{3}\right)=\cos \frac{\mathrm{\pi }}{6}=\frac{\sqrt{3}}{2}\\ \mathrm{\omega }=6280\Rightarrow 2\mathrm{\pi f}=6280\Rightarrow \mathrm{f}=1\mathrm{kHz}\\ \cos \mathrm{\varphi }=\frac{\mathrm{R}}{\mathrm{Z}}\text{ but }\mathrm{Z}=\frac{170}{8.5}=20\mathrm{\Omega }\\ \therefore \mathrm{R}=\mathrm{Zcos}\mathrm{\varphi }=20\times \frac{\sqrt{3}}{2}=10\sqrt{3}=17.32\mathrm{\Omega }\end{array}$

Since this circuit has voltage lagging behind the current, so this is RC circuit.

$$\begin{gathered} \begin{array}{l}{\mathrm{Z}}^2=\frac{1}{{\mathrm{\omega }}^2{\mathrm{C}}^2}+{\mathrm{R}}^2\Rightarrow 400=\frac{1}{4{\mathrm{\pi }}^2{\mathrm{f}}^2{\mathrm{C}}^2}+300\\ \Rightarrow 100=\frac{1}{(2\mathrm{\pi fC}{)}^2}\Rightarrow 2\mathrm{\pi fC}=0.1 \\ \Rightarrow C = \frac{1}{62800} = 15.92 \times {10}^{-6} \mathrm{F}\end{array} \end{gathered}$$