Ah, something a neurobiologist can answer! ( Its my Masters!)
Ok there are tons of types of Na K and Ca channels on a neuron membrane. These channels act as resistors on the membrane while the phospholipds of the membrane act as a capacitor. So thses two are in a parrallel circuit, thus the RC circuit of the membrane.
Now there are potassium channels that have a constant stochastic rate of opening despite any stimulus. These are the leak channels. They slowly let positive charge leak out of the cell. This only makes since, otherwise the NA-K-Atpase would continually hyperpolarize the cell past RMP. Now there is all types of math and physics here that is used to prove this and if your intrested I will PM you with the physical proof. So we have established the potassium leak current. This is the input resistance of the cell plus the charging capacitance of the cell.
Now we have a presynaptic neuron, lets say its glutamanergic, it stimulates AMPA receptors and then NMDA receptors causing a LOCAL depolarization. This is a GRADED potential. It undregoes volatage attenuation dependent on time and distance. Think of this a throwing a rock in a lake and the ripples that probagate from its epicenter. Those ripples are the graded potentials. As it goes along, if strong enough to reach a voltage sensaitive Na channel, it will activate it and more current will enter the cell and the graded potential will continue to flow. Only once threshold is reached does it become all or nothing. Threshold is when the inward current (Na) is equal to the outward current ( leak K). At this point the cell is more positive than the extacellular space. This only takes 3 chages according to the Hogkin and Huxley model. Then the graded charge is moving enough and the density of Na channels is high enough that an AP occurs (usually at the axon hillock).
If you want to know about the synaptic transmission that occurs next with the monoamine and neuropeptide transmitters PM me.
What is really interesting is what happens when the receptor sub types are activated ( Ltype Ca channels, the 3 other voltage gatted Na channels some of which are slow activating and noninactivating, the oth K channels, Cl channels) it takes the basic concept of AP's and screws it all up to where you get pacemaker potentials, burst firing, sensitization....
