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The impedance magnitude of a linear electrical circuit in sinusoidal steady state is the ratio of voltage amplitude to electric current amplitude. For complex impedance $Z=R+iX$, it is $|Z|=\sqrt{R^2+X^2}$, whereas the dissipative electrical resistance is $\mathrm{Re}Z=R$. Measuring only amplitudes does not separately determine $R$ and $X$; a phase shift measurement supplies the missing information.

At direct current an ideal capacitor is an open circuit. A finite measured electrical resistance therefore requires the resistor and capacitor to form a parallel circuit, with $R=100\Omega$. Use phasors proportional to $e^{i\omega t}$. The electrical admittance and complex impedance areInterpreting the stated AC value as the measured impedance magnitude, $\omega =2\pi (50){\mathrm{s}}^{-1}$ and $|Z|=20\Omega$ give $\omega RC=\sqrt{24}$. ThusThe electric current leads the applied voltage by ${\tan }^{-1}\sqrt{24}=78.46^{\circ }$. Strictly, AC “resistance” is ambiguous: if it means $\mathrm{Re}Z=20\Omega$, the same parallel circuit instead gives $\omega RC=2$, $C=63.7\mu \mathrm{F}$, and $Z=20-40i\Omega$. A measurement of $|V|/|I|$ selects the boxed interpretation.