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Electrostatic Potential And Capacitance

Question

The space between the plates of a parallel plate capacitor is filled consecutively with two dielectric layers of thickness d₁ and d₂ having relative permittivities ε₁ and ε₂respectively. If A is area of each plate, what is the capacity of the capacitor?

Solution

Capacitance is given by C=

\frac{ε_{\circ} A}{d}

As, effective thickness of dielectric is 1/ε times the actual thickness, therefore, the capacity of condenser is

C = \frac{\in_{0} A}{\frac{d_{1}}{\in_{1}} + \frac{d_{2}}{\in_{2}}}