Solution
= Solution
The source diagram has $2R$ in series with two parallel branches: $R+L$ above and $R+C$ below. With $s=\sqrt{15}$, their <complex impedances> are $Z_+=R(1+is)$ and $Z_-=R(1-is)$. Their parallel combination is
$$
Z_p=\frac{Z_+Z_-}{Z_++Z_-}=\frac{R^2(1+s^2)}{2R}=8R.
$$
Thus
$$
\boxed{Z_{AB}=2R+8R=10R.}
$$
The input <electric current> is in phase with $V_{AB}$ even though the two branch currents separately have nonzero, opposite phase shifts.