The equation for the voltages in a driven RLC circuit can be put into the form:
I Z cos(wt+ϕ) = I Xc cos(wt – π/2) + I R cos(wt) + I XL cos(wt + π/2)
Where I is the maximum current, Z the impedence, Xc the capacitive reactance (1/wC), XL the inductive reactance (wL), and w the angular frequency. (One or more of these terms may be missing in a simpler circuit.) (The I's can be divided out.) Either way, this equation resembles the equation for adding the x components of three vectors to get the x component of the resultant vector. (As function of time, all four (imaginary) vector are rotating around the origin of thean xy coordinate system. As they rotate, the x components represent the instantaneous voltage on the corresponding circuit element and their angular separation represents the phase difference.) To simplify the calculation of Z and ϕ, the vectors are generally sketched at t = 0. The rotating vector are just a way of representing trig functions which are out of phase. (Only the x components are significant.) In more advanced courses you may see the vectors in the complex plane represented by imaginary exponential functions. As in this case, only the real components are significant These may be used to represent wave functions as well as circuit voltages.