## 2 Photovoltaics MCF Rubber Solar Cell  
An ordinarily solar cell is evaluated with an equivalent electric circuit comprising a capacitor and resistor, as shown by Figure 1. First, we investigate the resistance \(R\), and the total resistance of the solar cell in which there exists some internal resistances. The experimental data of \(R\) in a wet-type MCF rubber solar cell is shown in Figure 2 under elongation and compression. Figure 2a,b shows the amplitude of tension and Figure 2c,d shows that of pressure. The experimental apparatus and procedure were the same as those used in the second report [19]. In general, the voltage and current of the solar cell have both photo and built-in electricity. The former and the latter causes were explained previously in the second report. Therefore, resistance can be estimated to be divided between the two cases. At a lesser elongation, by compression, the photovoltaic resistance is almost constant; however, the built-in voltaic resistance increases. At a greater elongation, by compression, both resistances decrease or remain constant. On the other hand, by elongation, both resistances have a peak in the linear elastic region of the MCF rubber, and then decrease in the plastic region. In contrast, tunneling theory is applicable to the MCF rubber solar cell. The transfer of electric current over the potential barrier of the rubber under compression as a one-dimensional Schrodinger equation is easier because of the decreasing size of the gap of the insulator, as shown previously in the first report [17]. From the equations presented in the report, the resistance \(R\) of the MCF rubber solar cell is given by Equation (1) with a transmitted probability of \(T\), where \(eE_{o}\) is the applied voltage, \(e\) is the elementary charge, \(\gamma\) is the wave number presented by Equation (2), \(\hbar\) is \(h/2\pi\), \(h\) is [PERSON]'s constant, \(m\) is the mass of the electron, \(V_{o}\) is the potential energy at region \(\gamma\) for each \(i\)-ordered pair of regions fabricated with non-conductive rubber sandwiched by conductive materials, and \(\varepsilon\) is the energy of the electron. At each \(i\)-ordered pair of regions, the transmitted current is given as the denominator of the middle expression of Equation (1)  
Figure 1: Equivalent electric circuit with capacitance \(C\) and resistance \(R\) of a magnetic compound fluid (MCF) rubber solar cell. and approximately evaluated as \(T_{out}\), which is \(T\) at the outlet of \(n\) pairs of regions through which the electrons transfer. \[R=\frac{eE_{o}}{\sum\limits_{i=1}^{n}T_{i}\Big{(}\frac{\gamma_{i}}{\gamma_{i+1}}- \frac{\gamma_{i+1}}{\gamma_{i}}\Big{)}}\cong\frac{eE_{o}}{T_{out}} \tag{1}\]  
\[\gamma=\sqrt{\frac{2m}{\hbar^{2}}(V_{o}-\varepsilon)} \tag{2}\]  
Figure 2: Changes in the effect of compression and elongation on resistance based on the photovoltaic effect and built-in electricity under ultraviolet light. (**a,b**) under compression; (**c,d**) under elongation; (**a,c**) based on photovoltaic effect; (**b,d**) based on built-in electricity for a wet-type MCF rubber solar cell electrolytically polymerized under a magnetic field with 0.22 g of Ruthenium complex dye and 7.4 g of KI+I\({}_{2}\) electrolyte. The MCF rubber had 3 g of TiO\({}_{2}\), 6 g of Ni, 4.5 g of MF, and 9 g of natural rubber (NR)-late. The irradiation light was ultraviolet (40 lx). As a result, dimensionless resistance \(R^{*}\) (=\(R/R_{\infty}\), \(R_{\infty}\) the representative resistance) to compressive strain \(cs\) is given by Figure 3. At a high tensile strain, the resistances based on both the photovoltaic effect and built-in voltage decrease with increasing compressive strain. The tendencies in Figure 2a,b can be explained by the theoretical results of Figure 3. However, the properties of these resistances in Figure 2c,d at low tensile strain cannot be explained by the present tunneling theory, and are due to the complicated fabrication of particles involved in the MCF rubber solar cell.