Question

A parallel plate capacitor is of area $6 \; cm^2$ and a separation $3\, mm$. 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 when fully inserted in above capacitor, gives same capacitance would be :

• A. 12
• B. 4
• C. 36
• D. 14

Answer 1

Answer: (A)

12

Answer 2

Let dielectric constant of material used be K.
$\therefore \frac{10\in_{0} A/3}{d} + \frac{12\in_{0} A/3}{d} + \frac{14\in_{0} A/3}{d} =\frac{K\in_{0} A}{d}$
$\Rightarrow K = 12$