﻿ Capacity in the alternating current circuit

# Value of alternating-current capacity

The direct current cannot pass through capacity as its facings are separated by isolation.

Block diagram of the alternating current generator.

But if capacity With is included under the alternating voltage, then its charge of q — Cu changes depending on tension size. Owing to these changes of the charge of capacity in the conductors connecting this capacity to the source of alternating voltage there is the movement of charges.

At increase in the charge of capacity they will move to one party, at reduction — in opposite.

Phase of sine wave voltage.

Such progressive and returnable movement of charges represents alternating current:

i = ? q/? t = C (? u: ? t),

where? t - very small period during which tension changes on? u, and the charge on? q.

Period? t has to be very small in order that it was possible to consider the relation (? u: ? t) to constants and to remove certain dependences between current and tension.

If tension sinusoidalno u = Um sin? t , in time? t it changes on:

u = Um sin ? (t + ? t) -  Um sin ? t,

In this expression:

sin? (t + ? t) = sin? t cos ?? t + cos? t sin?? t,

and as corner?? t  is very small, its sine is equal to the arch, and the cosine unit:

sin?? t = ?? t,  cos ?? t = 1,

on the basis of what:

u = Um sin ? t + Um ?? t cos?  t-Um sin ? t = Um ?? t cos? t or

(? u: ? t) = Um ? cos? t

Therefore, through capacity there passes alternating current:

i = Um ? With  cos? t

As:

cos? t = sin (? t + ?/2) = sin? (t + ?/2),

that this current advances on the phase sine wave voltage by the quarter of the period (fig. 1).

It is easy to find the ratio between the operating values of tension and current intensity in the capacity chain. In the right part of expression of current intensity only cos depends on time? t. Its amplitude value is unit. Therefore, the maximum value of the alternating current passing through capacity will be:

ImUm? With

Having replaced the maximum values with operating: