Electrostatic Potential And Capacitance Ques 40
40. A parallel plate condenser with oil between the plates (dielectric constant of oil $K=2$ ) has a capacitance $C$. If the oil is removed, then capacitance of the capacitor becomes
[1999, 97]
(a) $\sqrt{2} C$
(b) $2$ $ C$
(c) $\frac{C}{\sqrt{2}}$
(d) $\frac{C}{2}$
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Answer:
Correct Answer: 40.(d)
Solution:
- (d) When oil is placed between space of plates
$C=\frac{2 A \varepsilon_0}{d} $ $\quad$ …….(i)
$[\because C=\frac{K A \varepsilon_0}{d}$, if $K=2]$
When oil is removed $C^{\prime}=\frac{A \varepsilon_0}{d}$ $\quad$ …….(ii)
On comparing both equations, we get $C^{1}=C / 2$
When dielectric is partially filled between the plates of a parallel plate capacitor then its capacitance increases but potential difference decreases. To maintain the capacitance and potential difference of capacitor as before separatoin betweeen the plates has to be increased by d. In such case
$ k=\frac{t}{t-d} \text{ (Here, } t=\text{ seperation between plates.) } $
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