A) 40
B) 20
C) 30
D) 10
Correct Answer: D
Solution :
The arrangement of n metal plates separated by dielectric acts as parallel combination of \[(n-1)\] capacitors. Therefore, \[C=\frac{(n-1)K{{\varepsilon }_{0}}A}{d}\] Here, \[C=100pF\] \[=100\times {{10}^{-12}}F\] \[K=4,\,{{\varepsilon }_{0}}=8.85\times {{10}^{-12}}{{C}^{2}}/N{{m}^{2}}\] \[A=\pi {{r}^{2}}=3.14\times {{(1\times {{10}^{-2}})}^{2}}\] \[d=1mm=1\times {{10}^{-3}}\] \[(n-1)\times 4\times 8.85\times {{10}^{-12}}\] \[\therefore \] \[100\times {{10}^{-12}}=\frac{\times 3.14\times {{(1\times {{10}^{-2}})}^{2}}}{1\times {{10}^{-3}}}\] or \[n=\frac{1111.156}{111.156}\] \[=9.99\] \[\approx 10\]
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