Electrostatics 5 Question 14
15. A parallel plate capacitor is of area $6 \mathrm{~cm}^2$ and a separation 3 $\mathrm{mm}$. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants $K_1=10$, $K_2=12$ and $K_3=14$. The dielectric constant of a material which give same capacitance when fully inserted in above capacitor, would be
(Main 2019, 10 Jan I)
(a) 4
(b) 36
(c) 12
(d) 14
Show Answer
Answer:
Correct Answer: 15. (c)
Solution:
- In the given arrangement, capacitor can be viewed as threedifferent capacitors connected in parallel as shown below,
So, equivalent capacity of the system is
$ \begin{aligned} C_{\mathrm{eq}} & =C_{1}+C_{2}+C_{3} \\ \Rightarrow \frac{K \varepsilon_{0} A}{d} & =\frac{K_{1} \varepsilon_{0} A / 3}{d}+\frac{K_{2} \varepsilon_{0} A / 3}{d}+\frac{K_{3} \varepsilon_{0} A / 3}{d} \\ \Rightarrow \quad K & =\frac{K_{1}}{3}+\frac{K_{2}}{3}+\frac{K_{3}}{3} \\ \text { Here, } K_{1} & =10, K_{2}=12 \text { and } K_{3}=14 \\ \text { So, } \quad K & =\frac{10+12+14}{3} \Rightarrow K=12 \end{aligned} $
