Two parallel plate air capacitors of same capacity ′ C ′ are connected in series to a battery of emf ′ E ′ . Then one of the capacitors is completely filled with dielectric material of constant ′ K ′ . The change in the effective capacity of the series combination is

Home » Two parallel plate air capacitors of same capacity ′ C ′ are connected in series to a battery of emf ′ E ′ . Then one of the capacitors is completely filled with dielectric material of constant ′ K ′ . The change in the effective capacity of the series combination is

Physics | Physics

Two parallel plate air capacitors of same capacity ′ C ′ are connected in series to a battery of emf ′ E ′ . Then one of the capacitors is completely filled with dielectric material of constant ′ K ′ . The change in the effective capacity of the series combination is

Solution: the correct answer is D.

$\frac{1}{{{C}_{initial}}}=\frac{1}{C}+\frac{1}{C}$

${{C}_{initial}}=\frac{C}{2}$

$\frac{1}{{{C}_{final}}}=\frac{1}{KC}+\frac{1}{C}$

${{C}_{final}}=\frac{CK}{K+1}$

${{C}_{final}}-{{C}_{initial}}=\frac{C}{2}\left[ \frac{K-1}{K+1} \right]$

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