As we know the impedance offered by capacitor (capacitive reactance) Xc=1/(2*pi*f*c).For D.C the frequency f=0,there for impedance offered by capacitor will be infinite.And D.C current is blocked and it doesn't flow.while in the case of A.C the frequency is not zero,hence it allows A.C current.
In the case of charging of capacitor,it will charge fully to the D.C voltage across it.Then it will not discharge and remains in the same voltage which applied across the capacitor.Hence there will be no potential difference and also no current flow through it.In the case of A.C , the voltage is gradually increases and reaches a maximum value and then decreases and reach a maximum value in opposite direction and so .At this time the capacitor also charge to maximum and then discharges and again charged in opposite direction and so on.Hence An A.C current will flow through the capacitor.
There is another equation which regarding to capacitor is that capacitor current Ic=c*dv/dt..where dv/dt is the rate of change of voltage.In the case of D.C, the voltage is constant (steady) hence the term dv/dt =0,So the equation becomes Ic=c*0=0.So no current will flow through it.While in the case of A.C dv/dt is not constant and there is always a current flow through the capacitor.
In the case of charging of capacitor,it will charge fully to the D.C voltage across it.Then it will not discharge and remains in the same voltage which applied across the capacitor.Hence there will be no potential difference and also no current flow through it.In the case of A.C , the voltage is gradually increases and reaches a maximum value and then decreases and reach a maximum value in opposite direction and so .At this time the capacitor also charge to maximum and then discharges and again charged in opposite direction and so on.Hence An A.C current will flow through the capacitor.
There is another equation which regarding to capacitor is that capacitor current Ic=c*dv/dt..where dv/dt is the rate of change of voltage.In the case of D.C, the voltage is constant (steady) hence the term dv/dt =0,So the equation becomes Ic=c*0=0.So no current will flow through it.While in the case of A.C dv/dt is not constant and there is always a current flow through the capacitor.
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