Capacitive Reactance: Calculate Xc & V=I*Xc

[Devil Moo]

Hi,

A pure capacitor C is in an a.c. circuit.

Vc = V0 * sin(w*t)
Q = C * Vc
= C * V0 * sin(w*t)
I = dQ/dt
= wCV0 sin(wt)
then I0 = wCV0
Xc = V0 / I0 = 1/(wC)

So why people would say V = I * Xc?

Is it a must to include complex number?

 

[nasu]

The derivative of sin is cos.

You don't need complex numbers.

 

[Devil Moo]

Whoops!
I = I0 cos(wt)
Then V = I * Xc * tan(wt)
not V = I * Xc

 

[nasu]

The relationship V=I*Xc (with real numbers) is between the amplitudes or rms values and not between instantaneous values.
Otherwise you need to consider Xc as a complex number, to take into account the phase difference between v and i.

 

[Devil Moo]

But why do we introduce imaginary root in it?
Is it used to describe the phase based on the e^(i*theta)?