Engineering Finding Phase Difference in an RC circuit

[TheBigDig]

Homework Statement

Homework Equations

$V = ZI$
$Z_R = R$
$Z_C = -\frac{j}{\omega C}$
$Z = \sqrt{R^2 + (\frac{1}{\omega C})^2}$
$P_{av} = \frac{1}{2}V_m I_m cos(\phi)$
$\phi = arctan(\frac{-1/\omega C}{R})$
$\Delta \phi = \phi _1 -\phi _2$

The Attempt at a Solution

I've found what I believe to be the solution to the first part $Z_{in} = Z_R + Z_C = 5\Omega - 3.97j \Omega$ and the admittance which is $Y = \frac{1}{Z}$

For part b, I calculated the magnitude of Z and got $Z = 6.83 \Omega$ and then found the current using $I_m = \frac{V_m}{Z}$ = 1.57A. I calculated $\phi = -38.4^o$ and got a power of $6.15W$.

For part c, I'm stuck on finding the phase difference ($\Delta \phi$) because I'm not sure how to find another value of $\phi$ and there is none specified in the question. Any help would be appreciated.

 

[Hesch]

I_i = I_o = V_i/(R - j/ωC)

V_o = I_o * ( -j/ωC )

Phase shift = Φ , where Φ is calculated from V_o/V_i = xxxx∠Φ ( result in polar notation )

You may find an easier way, but this is the "basic" method.