Полное сопротивление ткани Z включает активное R и емкостное 1/ωC сопротивления. Обозначим Z1 – сопротивление здоровой ткани, Z2– сопротивление воспаленной ткани.
\[ Z = \sqrt {{R^2} + {{\left( {\frac{1}{{\omega C}}} \right)}^2}} . \]
\[\begin{gathered}
\frac{{{Z_1}}}{{{Z_2}}} = 4 = \frac{{\sqrt {{R^2} + {{\left( {\frac{1}{{\omega {C_1}}}} \right)}^2}} }}{{\sqrt {{R^2} + {{\left( {\frac{1}{{\omega {C_2}}}} \right)}^2}} }},\;\;\omega = 2\pi f \Rightarrow \;16 = \frac{{{R^2} + {{\left( {\frac{1}{{2\pi f{C_1}}}} \right)}^2}}}{{{R^2} + {{\left( {\frac{1}{{2\pi f{C_2}}}} \right)}^2}}}\;,\;\;\;\;{R^2} + {\left( {\frac{1}{{2\pi f{C_2}}}} \right)^2} = \frac{{{R^2} + {{\left( {\frac{1}{{2\pi f{C_1}}}} \right)}^2}}}{{16}}\; \hfill \\
{\left( {\frac{1}{{2\pi f{C_2}}}} \right)^2} = \frac{{{R^2} + {{\left( {\frac{1}{{2\pi f{C_1}}}} \right)}^2}}}{{16}} - {R^2},\;\;{\left( {\frac{1}{{2\pi f{C_2}}}} \right)^2} = \frac{{{{\left( {\frac{1}{{2\pi f{C_1}}}} \right)}^2} - 15{R^2}}}{{16}} \hfill \\
{C_2}^2 = \frac{{16}}{{{{\left( {2\pi f} \right)}^2}\left[ {{{\left( {\frac{1}{{2\pi f{C_1}}}} \right)}^2} - 15{R^2}} \right]}} = \frac{{16}}{{\frac{1}{{{C_1}^2}} - 15{{\left( {2\pi f} \right)}^2}{R^2}}} = \frac{{16 \cdot {C_1}^2}}{{1 - 15{R^2}{{\left( {2\pi f} \right)}^2}{C_1}^2}} \hfill \\
{C_2} = \sqrt {\frac{{16 \cdot {C_1}^2}}{{1 - 15{R^2}{{\left( {2\pi f} \right)}^2}{C_1}^2}}} = 4{C_1} \cdot \sqrt {\frac{1}{{1 - 15{R^2}{{\left( {2\pi f} \right)}^2}{C_1}^2}}} . \hfill \\
{C_2} = 4 \cdot 2,5 \cdot {10^{ - 6}}\sqrt {\frac{1}{{1 - 15 \cdot {{25}^2}{{\left( {2\pi \cdot {{10}^3}} \right)}^2} \cdot {{2,5}^2} \cdot {{10}^{ - 12}}}}} = 10,9 \cdot {10^{ - 6}}. \hfill \\
\end{gathered} \]
Ответ: 10,9 мкФ.
