Post-synaptic potentials produced in the dendrites can propagate to the soma to trigger action potentials. Throughout the cell, we also have passive channels that remain partly open all the time, leading to a leakage resistance. The insulating cell membrane separates the conductive cytoplasm inside the cell from the salt water environment outside, giving rise to a membrane capacitance. As the cytoplasm has some resistance, we also have an axial resistance along the dendrites and axon (not visible in this picture). Thus, a section of dendrite acts like a leaky cylindrical capacitor, coupled to neighboring sections with resistances.
In summary, we have a continuous distribution of resistance and capacitance across the membrane as well as an axial resistance parallel to the membrane. The various ion-selective channels across the membrane act like variable resistances.
The answer to our question is - we model it piece by piece. The usual approach is to model this with a lumped parameter model in which we divide the neuron into a finite number of compartments containing resistances, capacitances and batteries to represent ionic equilibrium potentials. We model this complex neuron with something like this.
Each of these compartments has an equivalent circuit that we will see in a minute.