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RC circuits - Phase diagram

In electronics, we often consider RC circuits. In particular, the processes occurring in RC circuits powered by sinusoidal voltage are analyzed. Such resistor-capacitor circuits can be used as various types of filters - a simple example is here.
Below you have a circuit consisting of a resistor R, a capacitor C and an electromotive force E. The value of the electromotive force is expressed by the function:

U(t) = U₀sin(ωt)
where: U₀ is the voltage amplitude, ω is the angular frequency expressed in radians per second and t is time (in seconds). The state of this circuit can be described by Kirchhoff's Second Law: U(t) = U_R(t) + U_C(t) and Ohm's Law: U_R(t) = I(t)R Appropriate mathematical considerations give the following results:

These mathematical functions are difficult to analyze. Therefore, it is often convenient to represent and analyze these functions in a phase diagram. Below is such the phase diagram for the RC circuit with the following parameters:

U₀ = 10V, R = 2k, C = 100nF, ω ≅ 4000      where: ω = 2πf (f - frequency). Therefore: f ≅ 637Hz, 1/ωC ≅ 2.5k, Phase shift φ ≅ -51.3 degs (0.895 rad) - you can use the calculator for series RC circuits.
The phasor diagram allows you to easily see and analyze the correlation between: U(t), U_R(t) and U_C(t).