Question

Between the plates of a parallel-plate capacitor of area A, a copper plate sits on a dielectric slab of k=2, as shown in Fig. 2.177. Find the equivalent capacitance of this arrangement​

Answer 1

Answer:

See answer in above attachment

Answer 2

Concept:

• Parallel plate capacitors
• Calculating equivalent capacitance

Given:

• Parallel plate capacitor has area A
• The copper plate has k = 2
• The thickness of the copper plate = d/3

Find:

• The equivalent capacitance of the arrangement

Solution:

First capacitance

C1 = 2εA/(d/3) = 6εA/d

Second capacitance

C2 = KεA/(d/3) =2εA/(d/3) = 6εA/d

Third capacitance

C3 = εA/(d/3) = 3εA/d

Net capacitance of capacitors connected in series.

1/C = 1/C1 +1/C2 +1/C3

1/C = d/6εA +  d/6εA +  d/3εA

1/C = d/6εA +  d/6εA +  2d/6εA

1/C = 4/6εA

1/C = 2/3εA

C = 3εA/2

The equivalent capacitance of the arrangement is 3εA/2.

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