MCQ
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant $K$ is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4} d$, where $'d'$ is the separation between the plates of parallel plate capacitor. The new capacitance $(C')$ in terms of original capacitance $\left( C _{0}\right)$ is given by the following relation
  • A
    $C ^{\prime}=\frac{3+ K }{4 K } C _{0}$
  • B
    $C ^{\prime}=\frac{4+ K }{3} C _{0}$
  • $C ^{\prime}=\frac{4 K }{ K +3} C _{0}$
  • D
    $C ^{\prime}=\frac{4}{3+ K } C _{0}$

Answer

Correct option: C.
$C ^{\prime}=\frac{4 K }{ K +3} C _{0}$
c
$C _{0}=\frac{\in_{0} A }{ d }$

$C ^{\prime}= C _{1}$ and $C _{2}$ in series.

i.e. $\frac{1}{ C ^{\prime}}=\frac{1}{ C _{1}}+\frac{1}{ C _{2}}$

$\frac{1}{ C ^{\prime}}=\frac{(3 d / 4)}{\in_{0} KA }+\frac{ d / 4}{\in_{0} A }$

$\frac{1}{ C ^{\prime}}=\frac{ d }{4 \in_{0} A }\left(\frac{3+ K }{ K }\right)$

$C ^{\prime}=\frac{4 K C _{0}}{(3+ K )}$981-s542

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free