# Capacitor charging in the first quater of the negative half cycle and discharging in the next half

#### kmohanra

Joined Feb 4, 2008
7
I try to understand the current behavior in capacitor when the AC source is connected. I have read many blogs in the internet to understand the concept of the charge flow in the capacitor when the ac is pass through it . In all the blog I have read, it starts with the +ve half cycle ac voltage and don't find very detailed and clear explanation for the negative half cycle.

I could follow the positive cycle of the ac voltage applied to the capacitor.
In the first +ve cycle ( 0 - 90 degree ) -- Voltage across the capacitor is 0 at t = 0. Hence the current starts from Max and reaches to 0 as the voltage across the capacitor starts build up which opposes the charge flow from the source.
In the first +ve cycle ( 90 - 180 degree ) -- Capacitor starts discharging the charge as the voltage across the capacitor > source voltage until it reaches the no charge state. Current reaches the negative peak now.
i(t) = C dv / dt

In the first -ve cycle ( 180 - 270 degree ) -- here i unable to get the point. when the voltage is dropping to more negative slope is negative. But the current tends to move to more positive ( -3, -2, -1 ). I am not able to follow this point. the voltage builds up in the capacitor should start opposing the voltage from the source. in this cast current should start decreasing but here it is increasing. My understanding is not correct. I try to visualize the current flow as if it happens in the complete 360 degree cycle. But i got stuck up here. Can some one please help to resolve my question with clear explanation of the current flow in the capacitor in the -ve cycle of AC source. please...

#### crutschow

Joined Mar 14, 2008
25,645
The current flow is similar in the negative cycle to the positive cycle, just the direction is reversed.
Remember capacitors can be charged to either a positive or negative voltage (at least non-polarized ones can be).
Thus on the first half of the negative cycle, current starts moving out of the capacitor, generating a negative charge on the capacitor.
Then on the second half of the negative half-cycle, current moves back into the capacitor so that it ends up with zero charge at the end of the half-cycle.

#### Jony130

Joined Feb 17, 2009
5,186
When we connected any empty capacitor to AC voltage from 0° to 90° the Capacitor is in charging phase. At 90° no current is flowing ( rate of change of a sine wave is very small at peak voltage so the current that is flow through the capacitor must also be small).
At 90° to 180° the capacitor start to discharge it self with the rate of change of a input voltages. Vin is connect parallel to the capacitor, so voltage on capacitor must be equal input voltages ( second Kirchhoff's law ). And when Vin reach 0V, capacitor voltage also reach 0V (discharge ends).
So we have empty capacitor (act like short circuit) so we have max current flow through the capacitor.
And from 180° to 270° the capacitor will again start the charging phase but in opposite direction. And again form 270° to 360° capacitor start to discharge
And this discharge process ends at 360° when voltage across capacitor reach 0V.

#### kmohanra

Joined Feb 4, 2008
7
in 180 deg - 270 degree, the capacitor starts charging in the opposite direction. When the capacitor starts charging, it should oppose the charge builds up as like in the positive cycle , but here it gets increasing which i am not still clear. may be still i do not get what you try to explain me. can you please elaborate the concept of current getting increased in 180 - 270 degree rather it decreasing. sorry to ask the fundamentals..can you please explain..

#### Jony130

Joined Feb 17, 2009
5,186
At 180 deg Vin = 0V and this is why Vc is equals to 0V (current is at his maximum). But now Vin "rise" into negative direction and this means that the capacitor will start the charging phase (exactly the same way as he did for the positive half but this time the voltage is negative, rising from 0V to -10V for example).
In this phase the current will flow into the capacitor from the voltage source. At 270 degree Vin and Vc reach his maximum negative value (-10V), and this ends the charging phase (current is 0A). But now (270 degree 360 degree) Vin start to "drop" into positive direction (from -10V to 0V). And capacitor start discharge phase, current flow out-off the capacitor into the source.

#### crutschow

Joined Mar 14, 2008
25,645
Your problem seems to be thinking there is some difference between positive versus negative capacitor operation.
What do you mean "it gets increasing" for negative voltages?
The capacitor does oppose charge buildup equally well for both positive and negative currents when starting from zero charge.
The only difference is that the capacitor voltage gets more negative for negative voltage/current, as compared to more positive for positive voltage/current.
The direction of current flow into a capacitor is strictly determined by the relative difference between the applied voltage and the voltage residing on the capacitor due to its charge.
Thus if the applied voltage is more positive than the capacitor voltage the current flow will be into the capacitor, and if the applied voltage is more negative than the capacitor voltage, the current flow will be out of the capacitor.

#### kmohanra

Joined Feb 4, 2008
7
Thank you for the immediate feedback. i was thinking about it in my mind for last two days but still i fail to understand this simple concept.
when the voltage builds up in the first +ve cycle of input voltage, current starts decreasing because of the charge builds up in the capacitor.
if i correlate the same analogy,
At 180 - 270 degree ( no charge in capacitor ) , the input voltage swings from negative to more negative. here too voltage builds up in the capacitor. but the current tends from more negative to less negative and reaches 0 at 270 degree. here why the voltage builds up in the capacitor does not oppose the input voltage. instead of current goes to more negative, it goes like less negative over the period of time and reaches 0 finally at 270 deg.

as i was thinking this point for past two days i am totally confused may be now. but with some more explanation from your side could make me to come out of the zone where i am drowned with wrong understanding.

#### crutschow

Joined Mar 14, 2008
25,645
I'm sorry but your explanation of your problem is not at all clear.
Your statement "why the voltage builds up in the capacitor does not oppose the input voltage. instead of current goes to more negative" does not make sense to me.

You seem to think negative voltage and current somehow behaves differently from positive voltage and current.
It doesn't.
Other than the value of the sign in from of the quantities, it behaves the same.