MHT CET · Physics · Capacitance
In a parallel plate capacitor with air between the plates, the distance ' \(\mathrm{d}\) ' between the plates is changed and the space is filled with dielectric constant 8 . The capacity of the capacitor is increased 16 times, the distance between the plates is
- A \(2 \mathrm{~d}\)
- B \(4 \mathrm{~d}\)
- C \(\frac{\mathrm{d}}{2}\)
- D \(\frac{\mathrm{d}}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{d}}{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{C}_1=\frac{\mathrm{A} \varepsilon_0}{\mathrm{~d}}\) ...(i)
\(\mathrm{C}_2=\frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}^{\prime}} \Rightarrow 16 \mathrm{C}_1=\frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}^{\prime}}\)
...(iii)
where \(\mathrm{d}^{\prime}\) the unknown separation.
Dividing (i) by (ii)
\(\frac{C_1}{16 C_1}=\frac{A \varepsilon_0}{d} \times \frac{d^{\prime}}{A \varepsilon_0}\)
\(\frac{8 \mathrm{~d}}{16}=\mathrm{d}^{\prime}\)
\(\therefore \quad \mathrm{d}^{\prime}=\frac{\mathrm{d}}{2}\)
\(\mathrm{C}_2=\frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}^{\prime}} \Rightarrow 16 \mathrm{C}_1=\frac{8 \mathrm{~A} \varepsilon_0}{\mathrm{~d}^{\prime}}\)
...(iii)
where \(\mathrm{d}^{\prime}\) the unknown separation.
Dividing (i) by (ii)
\(\frac{C_1}{16 C_1}=\frac{A \varepsilon_0}{d} \times \frac{d^{\prime}}{A \varepsilon_0}\)
\(\frac{8 \mathrm{~d}}{16}=\mathrm{d}^{\prime}\)
\(\therefore \quad \mathrm{d}^{\prime}=\frac{\mathrm{d}}{2}\)
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