The LR Series Circuit

Setting up the circuit. A resistor $R$ and an inductor $L$ are connected in SERIES to an AC source $v=v_0\sin\omega t$, so the SAME instantaneous current $i$ flows through both elements at every instant -- this shared current is the natural reference phasor to build the diagram around.

The two voltage phasors. The voltage across the resistor, $V_R=IR$, is IN PHASE with the current (Section 7.4), so its phasor is drawn along the same direction as the current phasor $I$. The voltage across the inductor, $V_L=IX_L$, LEADS the current by $90^\circ$ (Section 7.5), so its phasor is drawn at right angles to $I$, ahead of it in the direction of rotation.

Adding the two phasors. Since $V_R$ and $V_L$ are at right angles to each other, and the source voltage $v$ must equal their (phasor) sum at every instant, the resultant applied-voltage phasor $V$ is the diagonal of the rectangle formed by $V_R$ and $V_L$ -- found, by the Pythagorean theorem, as

Reading off the impedance. Comparing this with the Ohm's-law-shaped relation $V=IZ$ identifies the circuit's impedance directly:

The phase angle. The angle $\phi$ by which the resultant voltage phasor $V$ sits AHEAD of the current phasor $I$ (equivalently, the angle by which the current LAGS the voltage) is read off the same right-angled triangle as

$\tan\phi = \frac{V_L}{V_R} = \frac{IX_L}{IR} = \frac{X_L}{R}$ …