Question

Can you have an AC series circuit in which there is a phase difference of (a) 180° (b) 120° between the emf and the current?

Answer 1

Let us consider an AC series LCR circuit of angular frequency ω. The impedance of the circuit is given by,
$Z=\sqrt{R^2+{\left(\omega L-\frac{1}{\omega C}\right)}^2}$
The phase difference between V and I is given by,
$\tan \varphi =\left(\frac{\omega L-{\displaystyle \frac{1}{\omega C}}}{Z}\right)$
From the above formula, we can clearly see that
$\varphi \in \left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$
So, we cannot have a phase difference of 180° or 120°.