As far as I understand, when a neuron fires the action potential generated in a cell body reaches only the presynaptic part of the synapse, then triggers the transmitter to pass through the gap, and that transmitter causes the membrane in the postsynaptic part to open ion channels, pumps, etc ..., which generate a completely new electric potential that finally reaches the receiver cell.
So the electricity generated in a firing neuron never actually reaches receivers (not directly)?
Yes – electricity does pass through synapses if the link between the neurons in question is constituted by an electrical synapse.
There are two different types of synapses, chemical synapses and electrical synapses.
At a chemical synapse, an arriving pre-synaptic action potential indeed causes the release of neurotransmitters which carry the signal across the synaptic cleft to the subsynaptic membrane. This can effect an action potential in the postsynaptic neuron (among other things).
At an electrical synapse, on the other hand, ions do actually move from the presynaptic cell, through a gap junction channel, and to the postsynaptic cell, capable to cause a depolarization there.
Electrical synapses are found in many animals (including human). Due to their different characteristics, like the lack of neurotransmitter-related mechanisms and a significantly smaller synaptic cleft, they e. g. allow for a faster propagation of a signal between two neurons (while the signal decreases in strength due to the lack of gain). They occur as a part of neural structures which require fast signal transmission.
(While more technical details can be found in the referenced sources, it is helpful to review some of the basic concepts to avoid misconceptions:
It is sometimes (naively) assumed that the propagation of an action potential consists in a flow of electric charge along the axon, but what actually happens is that ions move through the membrane, i. e. roughly along an axis that is orthogonal to the direction of the signal. It is the action potential that moves along the axon. Thus, the original question is not to be taken to mean »Does the electric current that moves along the length of the axon also move through the synaptic cleft?«
Still – even if the flow of electric charge does not constitute the action potential, electricity can flow along the axon, as well. This is what happens in the case of saltatory conduction between the nodes of Ranvier in myelinated axons. It is generally referred to as an electrotonic potential.)
Does electricity pass through synapse?
No because ...
... when a neuron fires the action potential generated in a cell body reaches only the presynaptic part of the synapse, then triggers the transmitter to pass through the gap, and that transmitter causes the membrane in the postsynaptic part to open ion channels, pumps, etc ..., which generate a completely new electric potential that finally reaches the receiver cell.
So the electricity generated in a firing neuron never actually reaches receivers (not directly) ...
You actually answered your own question.
Keep in mind that neurotransmitter release and action potential are two different things. Sometimes the amount of neurotransmitter released are not enough to depolarize the postsynaptic membrane for an action potential to happen. Conversely action potentials can happen in the absence of neurotransmitter as it happens in many cells with peacemaking activity. Remember that action potentials are a result of the biophysical properties of the membranes where they are produced and of course this depends on the different ion channels present in that membrane. (Source)
Also think about the mechanic of the saltatory conduction:
Myelinated axons only allow action potentials to occur at the unmyelinated nodes of Ranvier that occur between the myelinated internodes. It is by this restriction that saltatory conduction propagates an action potential along the axon of a neuron at rates significantly higher than would be possible without the myelination of the axon (200 m/s compared to 2 m/s). As sodium rushes into the node it creates an electrical force which pushes on the ions already inside the axon. This rapid conduction of electrical signal reaches the next node and creates another action potential, thus refreshing the signal. In this manner, saltatory conduction allows electrical nerve signals to be propagated long distances at high rates without any degradation of the signal. Although the action potential appears to jump along the axon, this phenomenon is actually just the rapid, almost instantaneous, conduction of the signal inside the myelinated portion of the axon. (Source)
