It is often useful to know the phase angle $\varphi$ between the emf and the current. You can see from FIGURE 32.17 that

The current $I$ cancels, and we’re left with

FIGURE 32.17 The current is not in phase with the emf.

We can check that Equation 32.27 agrees with our analyses of single-element circuits. A resistor-only circuit has $X_{\text{}\text{L}}=X_{\text{}\text{C}}=0$ and thus $\varphi ={\text{tan}}^{-1}\left(0\right)=0\text{ rad}$. In other words, as we discovered previously, the emf and current are in phase. An AC inductor circuit has $R=X_{\text{C}}=0$ and thus $\varphi ={\text{tan}}^{-1}(\infty )=\pi \text{/}2\text{ rad,}$ agreeing with our earlier finding that the inductor current lags the voltage by $90\text{°}$.

Other relationships can be found from the phasor diagram and written in terms of the phase angle. For example, we can write the peak resistor voltage as

Notice that the resistor voltage oscillates in phase with the emf only if $\varphi =0\text{rad}$.