Electrostatics Question 547
Question: A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is $ A\ metre^{2} $ and the separation is$ t\ metre $ . The dielectric constants are $ k _{1} $ and $ k _{2} $ respectively. Its capacitance in farad will be [MNR 1985; DCE 1999; AIIMS 2001]
Options:
A) $ \frac{{\varepsilon _{0}}A}{t}(k _{1}+k _{2}) $
B) $ \frac{{\varepsilon _{0}}A}{t}.\frac{k _{1}+k _{2}}{2} $
C) $ \frac{2{\varepsilon _{0}}A}{t}(k _{1}+k _{2}) $
D) $ \frac{{\varepsilon _{0}}A}{t}.\frac{k _{1}-k _{2}}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
The two capacitors are in parallel so $ C=\frac{{\varepsilon _{0}}A}{t\times 2}(k _{1}+k _{2}) $
