Calculate the ratio of capacitance of two capacitor filled with dielectrics of same dimensions but of different values K and K/4 arranged in two ways as shown in figure (i) and (ii).(where, K= relative permittivity of the dielectric material between the plates)
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a
5 : 2
b
25 : 16
c
5 : 4
d
2 : 5
answer is B.
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Detailed Solution
Here, C1=e0K1A2d+ε0K2A2d=ε0KA2d+ε0KA8d Given: K1=K and K2=k4=ε0KAd12+18=ε0KAd4+18=5ε0KA8d … (i)and C2=ε0Ad2k1+d2k2=ε0Ad2k+d2k4=(2K)ε0A5d .....(ii)Dividing eqs. (i) by (ii)C1C2=5ε0kA8d2kε0A5d=5×52×8=2516