Combining Capacitors in Series & Parallel Video Lessons

Concept

# Problem: Two parallel plate capacitors are connected in series. Both are filled with a dielectric with constant K.One capacitor had plates of area A1 separated by distance d1, the other has plate of area A2 separated by distance d2. What is the total capacitance of the two connected in series?

###### FREE Expert Solution

For capacitors in series, the equivalent capacitance is:

$\overline{)\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{e}\mathbf{q}}}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{n}}}}$

or

For two capacitors:

$\overline{){{\mathbf{C}}}_{\mathbf{e}\mathbf{q}}{\mathbf{=}}\frac{{\mathbf{C}}_{\mathbf{1}}{\mathbf{C}}_{\mathbf{2}}}{{\mathbf{C}}_{\mathbf{1}}\mathbf{+}{\mathbf{C}}_{\mathbf{2}}}}$

The capacitance of a parallel plate capacitor:

$\overline{){\mathbit{C}}{\mathbf{=}}\frac{\mathbit{K}{\mathbit{\epsilon }}_{\mathbf{0}}\mathbit{A}}{\mathbit{d}}}$

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###### Problem Details

Two parallel plate capacitors are connected in series. Both are filled with a dielectric with constant K.One capacitor had plates of area A1 separated by distance d1, the other has plate of area A2 separated by distance d2. What is the total capacitance of the two connected in series?