A capacitor of 10µF capacitance whose plates are separated by 10mm through air and each plate has area 4cm2 is now filled equally with two dielectric media of K1 = 2, K2 = 3 respectively as shown in figure. If new force between the plates is 8N. The supply voltage is ______V.

Engineering

Physics

Parallel Plate Capacitor

Question

A capacitor of 10µF capacitance whose plates are separated by 10mm through air and each plate has area 4cm² is now filled equally with two dielectric media of K₁ = 2, K₂ = 3 respectively as shown in figure. If new force between the plates is 8N. The supply voltage is ______V.

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Given $C = \frac{ε_{0} A}{d} = 10 μF$

After filled dielectric medium

Both capacitor connected in parallel

C_New = C₁ + C₂

$= \frac{ε_{0} A_{1 / 2} K_{1}}{d} + \frac{ε_{0} A_{1 / 2} K_{2}}{d}$

$= \frac{ε_{0} A}{d} (\frac{K_{1} + K_{2}}{2})$

$= 10 (\frac{2 + 3}{2})$

C_new = 25 μF

Force between plate of capacitor $F = \frac{{CV}^{2}}{2 d}$

$F = 8 = \frac{{CV}^{2}}{2 \times 10 \times 10^{- 3}}$

$\frac{8 \times 2 \times 10^{- 2}}{25 \times 10^{- 6}} = V^{2}$

$= \frac{16}{25} \times 10^{4} = \frac{16}{25} \times 100 \times 100 = V^{2}$

V = 80