A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1, = 10, K2 = 12 and K3 = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

Question

A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1, = 10, K2 = 12 and K3 = 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

Tardigrade Admin · Accepted Answer

Let dielectric constant of material used be K. ∴ (10∈0 A/3/d) + (12∈0 A/3/d) + (14∈0 A/3/d) =(K∈0 A/d) ⇒ K = 12

12

4

36

14

Let dielectric constant of material used be K. ∴d10∈0​A/3​+d12∈0​A/3​+d14∈0​A/3​=dK∈0​A​ ⇒K=12

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