A parallel plate capacitor is of area $$6cm2$$ 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 equivalent capacitance would be :

Question

A parallel plate capacitor is of area $$6cm2$$  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 equivalent  capacitance would be :

Infinity Learn · Accepted Answer

Consider three dielectric connected in parallel $$combinationCnet=C1+C2+C3$$ ⇒kA∈$$0d=k1A3$$∈$$0d+k2A3$$∈$$0d+k3A3$$∈$$0d$$ ⇒kA∈$$0d=A$$∈$$03dk1+k2+k3$$ ⇒$$k=k1+k2+k33=12$$

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