When a metal plate of negligible thickness is introduced between the two plates of a capacitor at middle position. Now, capacitance of capacitor will be
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At initial condition,
Capacitance of a capacitor,
When a metal plate of negligible thickness is introduced between the plates of capacitor, then it is equivalent to two capacitor connected in series. The distance between the plates of new capacitor is 
and area of plates remains same.
Using Eq. (i), we get
Now, the effective capacitance 
in series is
Hence, capacitance remains same.
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