User:1sfoerster/sandbox2

Simulation
Was simulated at circuitlab.com.



Power Analysis
Power Analysis is rooted in the phasor domain! The phasor domain is limited to sinusoidal driving sources. This is why the discussion of RMS power and it's calculation is not part of this analysis.
 * $$\mathbb{V}_s = 120 \sqrt{2}\angle 2.09$$
 * $$\mathbb{I} = 15.9 \angle 1.73 $$
 * $$\mathbb{I}^* = 15.9 \angle -1.73 $$

if :$$\mathbb{V} = M_v\angle\phi_v\quad$$, and $$\quad\mathbb{I} = M_i\angle\phi_i$$ then
 * $$\mathbb{S} = \mathbb{V}\mathbb{I}^* = \frac{M_vM_i}{2}\angle(\phi_v - \phi_i) = \frac{120 \sqrt{2} * 15.9}{2}\angle(2.09 - 1.73)= 135\angle 0.36=126 + 47.6j$$

and
 * $$cos(.36) = .936$$

In summary

Intuition
ELI ... voltage leads the current through an inductor

Derivatives cause a lag ... a delay in time ... which is a positive angle in sinusoidal.