Equation for Resistor and Capacitor

What do you mean, "What is the equation of a resistor and capacitor when both are connected together in series and in parallel?" Do you want to know each circuit's impedance, time constant, or phase shift? Or all of them? The reactance of a capacitor is 1/(2*pi*f*C), but it's -90 degrees phase-shifted from a pure resistance, so the series or parallel combination of the two elements is a vector sum in the complex plane. Let's start with some notation: Z => impedance, Y => admittance, X=> reactance, R => resistance, G => conductance, B => susceptance, f => frequency, j => imaginary operator, C => capacitance, pi = 3.14157, Y=1/Z, Z=1/Y, X(c)= -j1/(2**pi*f*C), and G(c)= R/(R^2+X^2). For a series RC circuit, Z = R - j1/(2*pi*f*C). For a parallel RC circuit, Y = 1/Z = 1/(R - j1/(2*pi*f*C)). For series circuits, the current in each element is the same and therefore the voltage triangle drawn in the complex plane is the same as the impedance triangle. For parallel circuits, the voltage across each element is the same, so the current triangle is the same as the admittance triangle. Phase shift of voltage in a series circuit is inverse tangent(X(c)/R), and phase shift of current in a parallel RC circuit is inverse tangent(2*pi*f*C/G). Time constant of a series RC circuit is the time required for the voltage on a capacitor to charge up to 63.2% of the applied voltage: T=RC, T=> seconds, R=> ohms, C=> farads.

What are you trying to build? A filter? Please re-write your question or define your intentions. A simple RC series or RC parallel are filters. Combined they need to be balanced to obtain flat responses. Send a diagram including source input frequency range(s), input load, output response desired and output load Z if known. In a high level theory, having a series RC and a Vo across the parallel C with load R is the basic begining of a band pass filter. See T models. It depends on desired frequency response and matching source and load Z. More poles, faster roll off. See Chebechev formulas for references. Hope this helps point you in right direction.