A parallel plate capacitor has plate area \(40\text{ cm}^2\) and plates separation \(2\) mm. The space between the plates is filled with a dielectric medium of a thickness \(1\) mm and dielectric constant \(5\). The capacitance of the system is
Show Hint
- \(24ε_0\text{ F}\)
- \(\frac{3}{10}ε_0\text{ F}\)
- \(\frac{10}{3}ε_0\text{ F}\)
- \(10ε_0\text{ F}\)
The Correct Option is C
Solution and Explanation
Air gap $1$ mm: $C_1=\frac{\varepsilon_0A}{10^{-3}}=4\varepsilon_0$. Dielectric part: $C_2=\frac{5\varepsilon_0A}{10^{-3}}=20\varepsilon_0$.
Series: $C=\frac{4\times20}{24}\varepsilon_0=\frac{10}{3}\varepsilon_0$.
Final Answer:
Option (C). \[ \boxed{\text{(C)}} \]
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