http://i1226.photobucket.com/albums/ee410/jean28x/8b1ad092d9dd25a8f10f1672c0073d97.jpg

Vs = 480<0 rms.
P1 10^5 W; pf1 0.7 lagging; P2 5 × 10^4 W; pf2 0.95 leading.

I know how to calculate the capacitance with one load, but how do I work with the two loads? Do I find the capacitance of both and then add them up?

 

You have both lagging and leading power factor loads.

I suggest you proceed as follows:

1. Calculate the leading VARS for the leading pf load.
2. Calculate the lagging VARS for the lagging pf load which is presumably greater than the leading VARS in (1) above.
3. Calculate the effective lagging VARS - the difference between the values found in steps (1) & (2).
4. The required compensation capacitance must therefore provide the VARS calculated in step (3) to give an overall unity pf.