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Hello.
Maybe this is very basic and important question for circuit analysis. Please see the attached image.
KCL (Kirchhoff's Current Law) is applied to red arrowindicated point and I choose the convention that current flowing out from the point is positive.
 side of the capacitor is actually grounded thus its voltage is 0 and red arrow point is V.
I_{1} = V/R and I_{2} = C(dV/dt).
Substituting these to KCL as I_{1} + I_{2} = 0 give the right equation as
V/R + C(dV/dt) = 0
The solution of exponentially decaying with time constant of RC.
Until this problem is solved well. Good!
But what if I choose the direction of I_{2} in opposite way? In this case KCL becomes
V/R  C(dV/dt) = 0
and solution is not right. V increases forever!
Only solution to solve this problem is to accept the idea that C(dV/dt) is positive only when current is from + to  through the capacitor. But why? The current can go + to  in rounding circuit all the way. (It is counterclock wise direction here.)
Could you tell me why i = C(dV/dt) has positive polarity only when current is across the capacitor from + to negative? Is there any physical reason?
Maybe this is very basic and important question for circuit analysis. Please see the attached image.
KCL (Kirchhoff's Current Law) is applied to red arrowindicated point and I choose the convention that current flowing out from the point is positive.
 side of the capacitor is actually grounded thus its voltage is 0 and red arrow point is V.
I_{1} = V/R and I_{2} = C(dV/dt).
Substituting these to KCL as I_{1} + I_{2} = 0 give the right equation as
V/R + C(dV/dt) = 0
The solution of exponentially decaying with time constant of RC.
Until this problem is solved well. Good!
But what if I choose the direction of I_{2} in opposite way? In this case KCL becomes
V/R  C(dV/dt) = 0
and solution is not right. V increases forever!
Only solution to solve this problem is to accept the idea that C(dV/dt) is positive only when current is from + to  through the capacitor. But why? The current can go + to  in rounding circuit all the way. (It is counterclock wise direction here.)
Could you tell me why i = C(dV/dt) has positive polarity only when current is across the capacitor from + to negative? Is there any physical reason?
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