A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric strengths of air and glass are 30 kV/cm and 300 kV/cm, respectively. The maximum voltage (in kilovolts), which can be applied across the capacitor without any breakdown, is ______.

In the range: 17 - 20

Given parallel plate capacitor is



The capacitance of air will be C₁ = Aε₀/d

The capacitance of glass will be C₂ = 4Aε₀/d

Both the dielectrics are in series connection as the area of the plate is the same in both the dielectrics (air and glass)

The equivalent capacitance will be as follows

$\begin{array}{l}{C}_{eq}=\frac{C_1{C}_2}{C_1+C_2}=\frac{4A{\epsilon }_0}{5d}\\ D_n={\rho }_s=\frac{Q}{A}=\frac{CV}{A}\\ D_n=\frac{4A{\epsilon }_0}{5dA}V\\ D_n=\frac{4{\epsilon }_0}{5d}V\\ E_1=\frac{D_n}{{\epsilon }_0}=\frac{4}{5d}V\\ 30\times 10^5=\frac{4V}{5d}\Rightarrow V=\frac{30\times 5\times 5\times {10}^{-3}\times {10}^5}{4}\end{array}$

V = 18.75 kV