Electrostatics Question 801
Question: A capacitor has two circular plates whose radius are 8cm and distance between them is 1mm. When mica (dielectric constant = 6) is placed between the plates. The capacitance of this capacitor and the energy stored when it is given potential of 150 volt respectively are
Options:
A) $ 1.06\times {{10}^{-5}}F,1.2\times {{10}^{-9}}J $
B) $ 1.068\times {{10}^{-9}}F,1.2\times {{10}^{-5}}J $
C) $ 1.2\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J $
D) $ 1.6\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Area of plate$ =\pi r^{2}=\pi \times {{( 8\times {{10}^{-2}} )}^{2}} $
$ =0.0201m^{2} $
$ \text{and }d=1mm=1\times {{10}^{-3}}m $
Capacity of capacitor $ C=\frac{{\varepsilon _{0}}{\varepsilon _{r}}A}{d}=\frac{8.85\times {{10}^{-12}}\times 6\times 0.0201}{1\times {{10}^{-3}}} $
$ =1.068\times {{10}^{-9}}F $ Potential difference,
$ V=150\ \text{volt} $
Energy stored, $ U=\frac{1}{2}CV^{2}=\frac{1}{2}\times (1.068\times {{10}^{-9}})\times {{(150)}^{2}} $
$ =1.2\times {{10}^{-5}}J $
