What should be the sign of the voltage across the inductors while doing circuit analysis?
It depends on how you choose the direction of the current through an inductor or the voltage polarity.







simulate this circuit &ndash; Schematic created using CircuitLab

$$ u_L = L\dfrac{i_L}{dt}$$

For above circuit, if the current is increasing, then the voltage is increasing also, since the inductor wants to block any further current rising. 

Inverted sign example:







simulate this circuit

$$ u_L = -L\dfrac{i_L}{dt}$$