The question asks: A voltage of the form \$V=V_0 sin (ωt)\$ is applied across the network. Evaluate the phase shift between the voltage and the current flowing through the network. State whether the current leads or lags.

I've found the complex impedance – it is \$ Z=R + 1/jwC\$ where j is the imaginary unit, w is the angular frequency and C is the capacitance. I then found the modulus and angle of this impedance. However, I don't understand how I can relate this to current and find the phase difference.

Phasors confuse me as I'm not sure whether I should be taking the length of the voltage vector into account when calculating the angles. The complex exponential method, representing V as \$V_0e^{j(wt)} = Z *I_0e^{j(wt+\phi)}\$ confuses me as I don't know how to find Phi, with two unknowns \$ I_0 \$ and \$ V_0 \$ there.

My ultimate issue is that I'm receiving differing information from different sources. Some youtube guides are suggesting things different to my textbook. Guidance would be appreciated.

## Best Answer

\$V_0e^{j(wt)} = Z *I_0e^{j(wt+\phi)} = Z\times I_0 \times e^{j\omega t}\times e^{j\phi}\$

\$Z = \dfrac{V_0}{I_0}\times e^{-j\phi}=\dfrac{V_0}{I_0}\:\: \large \angle \small (-\phi)\$

Now express your original expression for \$Z\$ in magnitude and angle form:

\$Z=\small \sqrt {R^2+(1/\omega C)^2} \:\:\large\angle \small arctan(\frac{-1}{\omega RC})\$

and equate the angles.