In textbooks, it says that myelination doesn't really affect the time constant as tau=RC where R is the membrane resistance and C is the membrane capacitance. Myelin increases membrane resistance while decreasing membrane capacitance so there isn't really an overall effect on the time constant. However, during active regeneration of the action potential, the current only goes the path with least resistance i.e. the nodes of Ranvier, so wouldn't the R be the resistance of the node of Ranvier instead of the resistance of the entire membrane as stated in the textbooks? If this argument is correct then wouldn't myelination increases decreases time constant? Thanks!
No. When a signal is sent through a myelinated axon, the Nodes of Ranvier act as repeaters in electronics. The signal/action potential will disperse down the axon, the Node of Ranvier will pick up the signal, amplify it, and send it to the subsequent Node of Ranvier. I think you're thinking of the Nodes of Ranvier as cracks in the myelin/axon rather than as mini re-amplification sites.