From the perspective of managerial accounting how do we classify electricity expenses for a manufacturing factory unit- fixed or variable and why.

It can be either. The electricity to run the basic stuff would presumably be about equal all the time and therefore be fixed. But if you, say, run machines that use a lot of electricity, it can be variable based on usage of the machine. You'd have to have an estimate of the usage of said machine for a certain output of product in order to figure out the variable cost.

It will depend on what the electricity is used for, and whether the variable part of it is significant enough to separate it out. So actually, it can easily be a mixed cost.