What is the time constant when modeling a biological neuron?

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The first few paragraphs of the Wikipedia article on time constants are incomprehensible for noobs like me, so let’s try to look for a more intuitive understanding of what a time constant is.
When we look at a neuron, the time constant is given formally by:
Now, let’s look at a single-compartment model of a neuron. This basically means that the neuron has a capacitance current, a membrane current and an input current.
The function for is then given by¹:
with being the equilibrium potential, resting potential or sometimes also called leak potential (sometimes denoted by ¹).

1) Miller, P. (2018) An Introductory Course in Computational Neuroscience. 1st edition. Cambridge, Masachusetts: The MIT Press.