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Two identical parallel plate capacitors, of capacitance \( C \) each, have plates of area \( A \), separated by a distance \( d \). The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants \( \mathrm{K}_{1}, \mathrm{~K}_{2} \) and \( \mathrm{K}_{3} \). The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig II.
If these two modified capacitors are charged by the-same potential \( \mathrm{V} \), the ratio of the emergy-stored in the two, would be \( \left(E_{1}\right. \) refers to capacitor (I) and \( \mathrm{E}_{2} \) to capacitor (ID))
(A) \( \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{\left(\mathrm{K}_{1}+\mathrm{K}_{2}+\mathrm{K}_{3}\right)\left(\mathrm{K}_{2} \mathrm{~K}_{3}+\mathrm{K}_{3} \mathrm{~K}_{1}+\mathrm{K}_{1} \mathrm{~K}_{2}\right)}{\mathrm{K}_{1} \mathrm{~K}_{2} \mathrm{~K}_{3}} \)
(B) \( \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{\left(\mathrm{K}_{1}+\mathrm{K}_{2}+\mathrm{K}_{3}\right)\left(\mathrm{K}_{2} \mathrm{~K}_{3}+\mathrm{K}_{3} \mathrm{~K}_{1}+\mathrm{K}_{1} \mathrm{~K}_{2}\right)}{9 \mathrm{~K}_{1} \mathrm{~K}_{2} \mathrm{~K}_{3}} \)
(C) \( \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{9 \mathrm{~K}_{1} \mathrm{~K}_{2} \mathrm{~K}_{3}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}+\mathrm{K}_{3}\right)\left(\mathrm{K}_{2} \mathrm{~K}_{3}+\mathrm{K}_{3} \mathrm{~K}_{1}+\mathrm{K}_{1} \mathrm{~K}_{2}\right)} \)
(D) \( \frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\frac{\mathrm{K}_{1} \mathrm{~K}_{2} \mathrm{~K}_{3}}{\left(\mathrm{~K}_{1}+\mathrm{K}_{2}+\mathrm{K}_{3}\right)\left(\mathrm{K}_{2} \mathrm{~K}_{3}+\mathrm{K}_{3} \mathrm{~K}_{1}+\mathrm{K}_{1} \mathrm{~K}_{2}\right)} \)
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