In a parallel plate capacitor of capacitance C, a metal sheet is … - Vidyadip

MCQ

In a parallel plate capacitor of capacitance $C$, a metal sheet is inserted between the plates, parallel to them. If the thickness of the sheet is half of the separation between the plates. The capacitance will be

A
$\frac{C}{2}$
B
$\frac{{3C}}{4}$
C
$4C$
✓
$2C$

✓

Answer

Correct option: D.

$2C$

d
(d) $C = \frac{{{\varepsilon _0}A}}{d}$ and $C' = \frac{{{\varepsilon _0}A}}{{\left\{ {d - \frac{d}{2} + \frac{{(d/2)}}{\infty }} \right\}}} = \frac{{2{\varepsilon _0}A}}{d}$
$==>$ $C' = 2C$

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