Capacitor is a charge storing device, The power across a resistor is given by

Now the capacitor can both supply and absorb voltage . so it means it can have both positive and negative values of Power . So the Power across capacitor can be some thing like a wave shown below

Now the question arises, that why does the values of power decreases, even if the voltage stays +ive. Or which factor , force the power to drop down to wards negative

Hence it means that value of power in a capacitor , does not depend on voltage but also on current value . so as the value of changes power sign also changes

Hence as the voltage and current in a capacitor varies from positive to negative values , the capacitor can be a element that absorbs or supplies energy, depending on the signs of +voltage and current

For this question we need to look at capacitor energy. We know integral of power with respect to time is energy

Hence the energy in a capacitor depends on voltage and not on current. Hence the value of current will not effect energy sign. Similarly the voltage in the formula has a square sign on it, which means , even if the voltage of value is negative , the square in the formula will convert it in to positive , which will yield positive energy, which shows that energy is being absorbed. Hence capacitor is a passive device

Determining Energy and Power across Capacitor .

For the above given capacitor , sketch power and energy graph.

We need to know the current , across capacitor as power is a function of voltage and current,

Finding Current

First lets divide the graph in time interval

Finding Slopes

Summarizing

Sketching Current

Sketching power

We know power is

Sketching

Sketching Energy

Formula

Inductor

The Power and Voltage across inductor is given by

Power Across Inductor

Energy Across Inductor