AC circuit

We know that in DC circuit, power can be simply expressed as the product of voltage and current: P=U*I.

Nevertheless, in AC circuit, this expression becomes a little more complicated. The power now is rephrased as "Complex Power", S=U*conjugate (I)=P+jQ.

Facts:
(1) Power factor: inductive loads have lagging power factor, capacitive loads have leading power factor.

The power factor is a ratio of real power to the apparent power, it's value is cos(theta), where theta is the angle between the current and the voltage of loads. If the current is lagging the voltage, we call it has a lagging power factor and vice versa.
Let's consider the inductive loads first (r+jwL). I=U/(r+jx). We will see that I=U/Z^2*(r-jx). If we assume the angle is 0 for U, then the angel of I is -90 degrees (if r is 0). Obviously it is lagging!
Now we consider the capacitive loads (r+1/jwC) . I=U/(r+1/jwC), then it is positive (leading) compared to voltage angle.

(2) Inductive loads absorb reactive power while capacitive loads produce reactive power.

Now that we know complex power S=P+jQ=U*conjugate(I). For inductive loads, S=U*conjugate(I)=U^2/Z^2 (r+jx) (note the sign is changed to + because it is conjugate). OK! Now we see that P is positive, Q is positive, which represent that the inductive loads absorb real power and reactive power. Similar for capacitive loads. The sign for the Q will be negative, indicating that they produce reactive power.
Another way to think about this:
I=Icos(theta)+jIsin(theta), S=U*conjugate(I)=U*(Icos(theta)-jIsin(theta)). Notice that if it is an inductive load, then theta<0, Q=-Isin(theta)>0, meaning that it absorbs reactive power. The derivation also applied to conductive loads.