Question

Three identical capacitors with same plate area and same plate separation of 1mm are filled with dielectrics of dielectric constant $k_1,k_2$ and $k_3$ having dielectric breakdown of $E_1,E_{2}and{E}_3$ respectively are arranged as shown in figure.
Given :
$k_1=2,E_1=3\times {10}^{6}v/m$
$k_2=4,E_2=20\times {10}^{6}v/m$
$k_3=5,E_3=5\times {10}^{6}v/m$

Maximum value of $E_o$ is $n\times {10}^3$ Volts, then n is

Answer 1

Maximum voltage across capacitor can be
$V_{max}=Ed$
So,
$V_{1max}=3\times {10}^{3}V$
$V_{2max}=20\times {10}^{3}V$
$V_{3max}=5\times {10}^{3}V$
By $V=\frac{Q}{C},V_1=2V_2$

Hence, $E_o=V_{1max}+V_2=3\times {10}^3+\frac{3}{2}\times {10}^3$ $E_o=4.5\times {10}^{3}V$