A parallel plate capacitor has plates of area $0.02\ \text{m}^2$ separated by $1\ \text{mm}$. Find its capacitance (a) with air between the plates, and (b) if the gap is completely filled with a dielectric of dielectric constant $K=5$.

A parallel plate capacitor has plates of area 0.02m² separated by 1mm. Find its capacitance (a) with air betwe

Example · Example 9

0.02\ \text{m}^2

(a) with air between the plates, and

(b) if the gap is completely filled with a dielectric of dielectric constant

K=5

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Given $A = 0.02\ \text{m}^2$ , $d = 1\ \text{mm} = 1\times 10^{-3}\ \text{m}$ .

(a) Without dielectric:

C_0 = \frac{\epsilon_0 A}{d} = \frac{(8.85\times 10^{-12})(0.02)}{1\times 10^{-3}} = 1.77\times 10^{-10}\ \text{F} = 177\ \text{pF}

(b) With dielectric ( $K=5$ ) filling the gap completely: …