Asnetcomp Tutorials: July 2012

The title is "Capacitance, Inductance and Time " but "Time" here is used as Frequency. The unit of Frequency is Hz as well as 1/s (1/t in symbol).

The relations between Capacitance and Frequency, Inductance and Frequency are commonly stated as below usually with no explanation.

$X= - \frac{1}{\omega C} = - \frac{1}{2\pi f C}$

or no <minus sign>

and

$X_L = \omega L = 2\pi f L\quad$

Two (2) very simple calculations lead to the above two equations.

1) Capacitance and Frequency

$X= - \frac{1}{\omega C} = - \frac{1}{2\pi f C}$

where X is Capative Reactance (Xc)

This relationship can be derived from the following basic Capacitor equation related with i and v.

$i(t)= \frac{\mathrm{d}q(t)}{\mathrm{d}t} = C\frac{\mathrm{d}v(t)}{\mathrm{d}t}.$

Rearranged

i (t) x dt
---------- = C
dv(t)

as I/V (or i/v) = 1/R

t/R = C

R = t/C

as Frequency (f) is 1/t or t = 1/f

R = 1/Cf

where R can be regarded as Xc and f is used as Frequency in general. ω = $2π$ f

We need some conceptional jump to get into another world of frequency domain.

2) Inductance and Frequency

Likewise,

$X_L = \omega L = 2\pi f L\quad$

where XL is Indcutive Reactance.

This relationship can be derived from the following basic Inductor equation related with i and v.

$v(t) = L \frac{di(t)}{dt}$

Rearranged

v (t) x dt
---------- = L
di(t)

as V/I (or v/i) = R

tR =L

R = L/t

as Frequency (f) is 1/t or t = 1/f

R = Lf

where R can be regarded as XL.

Here again we need some conceptional jump to get into another world of frequency domain.

ACT

Friday, July 13, 2012

Capacitance, Inductance and Time