Question

Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?

• A. $ \frac{KC}{(1+K)} $
• B. C (K + 1)
• C. $ \frac{2KC}{K+1} $
• D. None of these

Answer 1

Answer: (A)

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} $