An AC circuit connected to capacitor only

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An AC circuit connected to capacitor only

This circuit shows an AC circuit connected to capacitor only.

e=Emsinωt・・・（１）
q=Ce=CEmsinωt・・・（２）
q：charge on the capacitor in coulombs
C：capacitance of the capacitor in farads

When the alternnating voltage given by equation (1) is applied to this circuit, charge of the capacitor at any instant of time is given in equation(2).

The current i flowing through this circuit is the flow of charge out of the capacitor per unit time.

It is expressed as follows.

Xc(capacitive reactance)

1/ωC = Xc [Ω]
This is the formula for capacitive reactance.The Unit of Xc is orm.

1/ωC =1/2πfC =Xc
f：frequency in hertz
C：capacitance in farads

■POINT
The capacitive reactance decreases with increasing frequency.

The value will be at maximum

e=Emsinωt・・・（１）
q=Ce=CEmsinωt・・・（２）
i=Em/Xc sin(ωt+π/2)・・・（３）

When sinωt is equal to one, the value of e will be at maximum.

When sin(ωt+π/2) is equal to one, the value of i will be at maximum.

The current leads the voltage by π/2

From equation(1) and equation(3), it is clear that the current leads the voltage by π/2.

和訳