An air filled parallel plate capacitor initially has a capacitance of C = 2.01 n

Question

An air filled parallel plate capacitor initially has a capacitance of C = 2.01 nF.

Then the air gap between the plates is filled with two different dielectric materials with equal volume but with relative permittivities of E1= 2.14 and E2 = 9.96 respectively. In the first case the dielectric materials are formed into two layers parallel to the plates of the capacitor. (See figure.) Determine the capacitance of the capacitor. (Note: the relative permittivity denoted by ? is equivalent to thedielectric constant denoted by ?.)

In the second case the dielectric materials are formed into two blocks next two each other. (See figure.) What is the capacitance in this case?

An air filled parallel plate capacitor initially has a capacitance of C = 2.01 nF. materials with equal volume but with relative permittivities of E1= 2.14 and E2 = 9.96 respectively. In the first case the dielectric materials are formed into two layers parallel to the plates of the capacitor. (See figure.) Determine the capacitance of the capacitor. (Note: the relative permittivity denoted by ? is equivalent to thedielectric constant denoted by ?.) In the second case the dielectric materials are formed into two blocks next two each other. (See figure.) What is the capacitance in this case?

Explanation / Answer

1) C = ?0 A/d =2.01nF

C1 = E1*? 0*A/(d/2) = 8.6028 nF

C2 = E2*? 0A/(d/2) = 40.0392

Ceq= C1*C2/(C1+C2) = 7.0813 nF

2) C1 = E1*? 0*(A/2) / d = 2.15nF

C2 = E2*? 0*(A/2) / d=10 nF

Ceq = C1+C2 = 12.16 nF

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