How could be it possible to have the average current zero but the average power not equal to zero.....????

In one cycle of the AC when a resistor is connected with ana ac source the average of current in one cycle will be zero as it is a sinusoidal function but onecan imagine that power has to loose thrugh the heating effect as current is passing through a resistor even if there is a capacitor and a resistor is connected with an ac source the power consumed is through resistor only not through capacitor.