= Solution
Using the convention $e^{i\omega t}$, the series <RLC circuit> has <complex impedance>
$$
Z=R+i\left(\omega L-\frac1{\omega C}\right),\qquad\omega=2\pi f.
$$
At the stated <frequency>, $\omega L=180.956\,\Omega$ and $1/(\omega C)=88.4194\,\Omega$. Thus
$$
\boxed{\operatorname{Im}Z=+92.5\,\Omega,\quad |Z|=533\,\Omega,\quad\arg Z=+10.0^\circ.}
$$
The vector is $(525,92.5)$ in the resistance–<reactance> plane. Positive <reactance> means that the net circuit is inductive and current lags voltage. With the alternative $e^{-i\omega t}$ convention the imaginary signs reverse, while the magnitude and physical <phase> relationship agree.
\Image[/past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1-impedance.png]
{title=Series-circuit impedance in the resistance–reactance plane}
Back to article page
