AP EAMCET · PHYSICS · Capacitance
Two metal plates each of area ' \(A\) ' form a parallel plate capacitor with air in between the plates. The distance between the plates is ' \(d\) '. A metal plate of thickness \(\frac{d}{2}\) and of same area \(A\) is inserted between the plates to form two capacitors of capacitances \(C_1\) and \(C_2\) as shown in the figure. If the effective capacitance of the two capacitors is \(C^{\prime}\) and the capacitance of the capacitor initially is \(C\), then \(\frac{C^{\prime}}{C}\) is
- A \(4\)
- B \(2\)
- C \(6\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
We knows capacitance \(C=\frac{\varepsilon_0 A}{d}\) When plate is inserted \[ \begin{gathered} C^{\prime}=\frac{\varepsilon_0 A}{d-\frac{d}{2}}=\frac{2 \varepsilon_0 A}{d} \\ \frac{C^{\prime}}{C}=\frac{2}{1} \end{gathered} \]
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