How to Determine the voltage polarity of inductor in a circuit? The Voltage polarity across the inductor is same as that across the capacitor since both are in parallel and the voltage across them must be same.

But when Inductor, capacitor and resistor are connected as shown in the second figure what would be the voltage polarity across the inductor and why? (right end of inductor 'r'=+ve or -ve?)

 A: What might help (or not) here is to distinguish between reference polarity and absolute polarity.
When you label one terminal of the inductor with a plus sign, you're simply choosing a reference polarity.  You are, in essence, choosing which end to place the "red lead" of your voltmeter.
If you calculate that the voltage across the inductor is negative then you know the absolute polarity is opposite the chosen reference polarity.
This is no different from placing your voltmeter across the inductor and measuring a negative voltage; you know that the terminal connected to the "black lead" is more positive than the terminal connected to the red lead.
Similarly, you are free to choose a reference direction for the current in the circuit.  By the same argument as above, if you calculate (or measure) a negative current, you know the absolute direction is opposite the reference direction you chose.
By the passive sign convention, we choose have the current enter the positive labelled terminal so, in your example, the left of the inductor should be labelled positive and you should change the reference polarity of the capacitor.
By following this convention, when you calculate the power associated with a circuit element, the power will be positive if the circuit element is receiving power from the circuit and negative if the circuit element is supplying power to the circuit.
A: You don't need to worry about the convention you choose because the solution of the corresponding differential equation will automatically adjust the polarity. For the sake of simplicity, I usually use the passive convention as follows.

