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

• Correct answer
  A

  $\frac{C}{2}\left[\frac{K-1}{K+1}\right]$
• B

  $\frac{C}{4}\left[\frac{K-1}{K+1}\right]$
• C

  $\frac{C}{2}\left[\frac{K+1}{K-1}\right]$
• D

  $\frac{C}{2}{\left[\frac{K-1}{K+1}\right]}^2$

Hence, the correct answer is option: 'A'.