A parallel plate capacitor is of area 6 cm2 and a separation 3mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1 = 10, K2 = 12 and K3 = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

Engineering

Physics

Parallel Plate Capacitor

Question

A parallel plate capacitor is of area 6 cm² and a separation 3mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K₁ = 10, K₂ = 12 and K₃ = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

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C_net = C₁ + C₂ + C₃

$\frac{{kAE}_{0}}{d} = k_{1} (\frac{A}{3}) \frac{E_{0}}{d} + k_{2} (\frac{A}{3}) \frac{E_{0}}{d} + k_{3} (\frac{A}{3}) \frac{E_{0}}{d}$

$k = \frac{k_{1} + k_{2} + k_{3}}{3} = 12$