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 two 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) \[C=\frac{4{{\varepsilon }_{0}}A}{2\,d}=3\frac{6{{\varepsilon }_{0}}A}{2\,d}\] \[=\frac{2{{\varepsilon }_{0}}A}{d}+3\frac{{{\varepsilon }_{0}}A}{d}\] 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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