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Standard XII

Physics

Polarization Vector

Three identic...

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 $E_{1}, E_{2} a n d E_{3}$ 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

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Solution

Maximum voltage across capacitor can be
$V_{m a x} = E d$
So,
$V_{1 m a x} = 3 \times 10^{3} V$
$V_{2 m a x} = 20 \times 10^{3} V$
$V_{3 m a x} = 5 \times 10^{3} V$
By $V = \frac{Q}{C}, V_{1} = 2 V_{2}$

Hence, $E_{o} = V_{1 m a x} + V_{2} = 3 \times 10^{3} + \frac{3}{2} \times 10^{3}$ $E_{o} = 4.5 \times 10^{3} V$

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Maximum voltage across capacitor can be Vmax=Ed So, V1 max=3×103 V V2max=20×103 V V3 max=5×103 V By V=QC, V1=2V2 Hence, Eo=V1max+V2=3×103+32×103 Eo=4.5×103 V