A) 10\[\mu F\]
B) 5\[\mu F\]
C) 4\[\mu F\]
D) 7\[\mu F\]
Correct Answer: B
Solution :
Initially, the capacitance of capacitor \[C=\frac{{{\varepsilon }_{0}}A}{d}\] \[\therefore \] \[\frac{{{\varepsilon }_{0}}A}{d}=1\mu F\] ... (i) When it is filled with dielectrics of dielectric constants\[{{K}_{1}}\]and\[{{K}_{2}}\]as shown, then there are two capacitors connected in parallel. So, \[C=\frac{{{K}_{1}}{{\varepsilon }_{0}}(A/2)}{d}+\frac{{{K}_{2}}{{\varepsilon }_{0}}(A/2)}{d}\] (as area becomes half) \[C=\frac{4{{\varepsilon }_{0}}A}{2d}+\frac{6{{\varepsilon }_{0}}A}{2d}\] \[=\frac{2{{\varepsilon }_{0}}A}{d}+\frac{3{{\varepsilon }_{0}}A}{d}\] Using Eq. (i), we obtain \[C=2\times 1+3\times 1=5\mu F\]You need to login to perform this action.
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