A method is developed in order to determine the natural electrical thermal fluctuations and its spectral distribution across two points of a solution of ions or spherical charged particles immersed in an ionic solution. The electrical equivalent between two points of a solution is considered as a capacitor and a resistor in parallel, The method is applied within the Debye-Huckel approximation (linearized Poisson-Boltzmann equation), although it is valid in general, Among the results is the diminution of electrical fluctuations as particle sizes increase; as a consequence, large particles produce electrical stabilization in their neighborhood, It can also be observed that fluctuations are not quite sensitive to ionic concentrations for large particles. When the size of the particles become negligible we obtain similar results with the already obtained using the method of the mode expansion.