calculating the average power using the oscilloscope
To see phase shift you need to compare two separate wave forms. Looking at one wave form won't tell you anything. 



The two wave forms to compare are current and voltage. Seeing the voltage is easy, like you said, just connect the probe across the inductor. Seeing the current is more difficult because the oscilloscope can't "see" current. There are two options, use a current transducer to convert the current to voltage or use a resistor to do the same thing. Ohms law says that current through the resistor can be seen as a voltage drop across the resistor. 

Be careful, don't connect the oscilloscope grounds in different places. That's a fast way to burn up your scope. The problem with that is the wave forms will have an additional 180 degrees phase shift. Just compensate for it when you do the calculations. 







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