finding average power absorbed in each element. this is the work I have. webworks says its incorrect.

 

When the current and voltage are 90 degrees apart in an element, that element neither absorbs nor delivers power, but rather alternates between storing and deliver power, such that its net power absorption is zero. Thus, capacitors and inductors do not absorb power. Only resistors.

When the voltage and current are in phase, ie, resistors, then the element always absorbs power.

When the voltage and current are 180 degrees, ie, a battery, then the element always delivers power.

When voltage leads current 90 deg, then it's an inductor. Positive voltage makes current increase in the inductor. After the voltage reverses, the current begins to decrease, but it is still positive for 90 deg. And vice versa for negative voltage.

When current leads voltage 90 deg, then it's a capacitor. Positive current makes voltage increase across the capacitor. After the current reverses, the voltage begins to decrease, but it is still positive for 90 deg. And vice versa for negative current.

Voltage * Current in an inductor or capacitor is called var, volt-amperes reactive. Current is still flowing in the devices, and voltage exists between the nodes, but no power is being absorbed because of the 90 deg phase.

 

Without walking through your work in detail, just ask if the answers make sense.

You have one source that you claim is providing 966 W of power. Does that agree with the powers you are claiming the other components are absorbing?

No matter how I interpret your results, your power balances don't work out.

Always, always, ALWAYS ask if your answers make sense.

Before you started calculating any powers at all, you should check the results of your circuit analysis (the voltages and currents) to see if they are consistent with the problem statement. If they aren't, then anything you do after that is a waste of time that is guaranteed to produce incorrect answers.