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GUJCET · Physics · Electrostatic Potential and Capacitance
A parallel plate capacitor with air between the plates has a capacitance of 4 pF. If the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant 6, then the value of capacitance will be ________.
- A 98 pF
- B 24 pF
- C 12 pF
- D 48 pF
Answer & Solution
Correct Answer
(D) 48 pF
Step-by-step Solution
Detailed explanation
(D)
In absence of dielectric capacitance,
\(C _0=\frac{ A \varepsilon_0}{d}=4 pF\)
In presence of dielectric capacitance,
\(\begin{array}{l} C = K \frac{ A \varepsilon_0}{\frac{d}{2}} \\ C =2 K \frac{ A \varepsilon_0}{d}\end{array}\)
\(C =2 KC _0 \quad\left(\because \frac{A \varepsilon_0}{d}= C _0\right)\)
\(\begin{array}{l} C =2 \times 6 \times 4 \\ \quad\left(\because K=6 \text { and } C _0=4 pF \right) \\ C =48 pF \end{array}\)
In absence of dielectric capacitance,
\(C _0=\frac{ A \varepsilon_0}{d}=4 pF\)
In presence of dielectric capacitance,
\(\begin{array}{l} C = K \frac{ A \varepsilon_0}{\frac{d}{2}} \\ C =2 K \frac{ A \varepsilon_0}{d}\end{array}\)
\(C =2 KC _0 \quad\left(\because \frac{A \varepsilon_0}{d}= C _0\right)\)
\(\begin{array}{l} C =2 \times 6 \times 4 \\ \quad\left(\because K=6 \text { and } C _0=4 pF \right) \\ C =48 pF \end{array}\)
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