A) \[\frac{KC}{(1+K)}\]
B) C (K + 1)
C) \[\frac{2KC}{K+1}\]
D) None of these
Correct Answer: A
Solution :
When plates of capacitor are separated by a dielectric medium of dielectric constant\[K\], its \[{{C}_{m}}=\frac{K{{\varepsilon }_{0}}A}{d}=K{{C}_{0}}\] \[ie,\] \[{{C}_{m}}=K{{C}_{0}}\] Here, \[{{C}_{0}}=C\] \[\therefore \] \[{{C}_{m}}=KC\] Now, two capacitors of capacities\[KC\]and\[C\]are in series, their effective capacitance \[\frac{1}{C}=\frac{1}{KC}+\frac{1}{C}\] or \[\frac{1}{C}=\frac{1+K}{KC}\] \[\therefore \] \[C=\frac{KC}{K+1}\]
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