Capacitive Resistance:
Capacitive resistance, also known as capacitive reactance, is a term used to describe the opposition offered by a capacitor to the flow of alternating current (AC). It is denoted by the symbol Xc and is measured in ohms. Unlike resistors, which offer opposition to both AC and DC currents, capacitors only offer opposition to AC currents.

Variation of Capacitive Reactance with Frequency:
The capacitive reactance of a capacitor is inversely proportional to the frequency of the applied alternating voltage. The formula to calculate the capacitive reactance is given by Xc = 1 / (2πfC), where f is the frequency and C is the capacitance.

When the frequency is low, the capacitive reactance is high, and as the frequency increases, the capacitive reactance decreases. This relationship can be graphically represented as an inverse curve, where the x-axis represents the frequency and the y-axis represents the capacitive reactance.

As the frequency approaches infinity, the capacitive reactance tends to zero, indicating that at very high frequencies, the capacitor behaves like a short circuit.

Mathematical Analysis of Phase Angle:
To understand the phase relationship between the current and the applied voltage in a pure capacitor, we can use the concept of complex numbers. Let's consider an AC voltage E = E⁰sin(wt) applied across a pure capacitor of capacitance C.

Using Ohm's law, we can write the equation for the current flowing through the capacitor as I = E / Xc, where Xc is the capacitive reactance.

Substituting the value of Xc from the formula Xc = 1 / (2πfC), we get I = E / (1 / (2πfC)), which simplifies to I = 2πfEC.

Comparing this equation with the general form of current in an AC circuit, I = I⁰sin(wt + φ), we can conclude that the current in a pure capacitor leads the applied voltage by a phase angle of φ, given by φ = π/2.

Therefore, the current flowing through a pure capacitor leads the applied voltage by a phase angle of 2/π radians or 90 degrees.

Summary:
- Capacitive resistance refers to the opposition offered by a capacitor to the flow of AC current.
- Capacitive reactance varies inversely with the frequency of the applied voltage.
- The phase angle between the current and the applied voltage in a pure capacitor is 2/π radians or 90 degrees.