Does a VM eat up RAM even when the VM is not active?
Solution 1:
You don't specify which hypervisor you're using, but the general answer is no, if a VM is not running then it does not consume any CPU or RAM resources.
See it for yourself - open your task manager and go to the Performance tab while your VM is running. Then shut down your VM and watch your RAM usage drop.
Solution 2:
In general, a VM won't use RAM while the VM isn't "powered on."
It will use RAM when you're not interacting with it, if it is still powered on, and it may be hard to tell the difference in some cases between a VM that you're not connected to and one that's turned off.
Different virtualization systems may or may not use RAM when no VMs are in use. True hypervisors (of which Virtual Box is not one) will use some RAM when the hypervisor is active. If you're sitting at the "host" OS, and you have a hypervisor running, you'll have less RAM available than if you were not running a hypervisor. Hosted VMMs (like Virtual Box, VMWare Server, VMWare Player, Microsoft Virtual PC and Virtual Server) won't use any measurable RAM when no VMs are running.
It's often difficult to tell the difference between a "bare metal" hypervisor like VMWare ESX, Microsoft's HyperV or Xen and a hosted VMM.