A parallel plate capacitor with air between the plates has a...

A parallel plate capacitor with air between the plates has a capacitance of

9 \mathrm{pF}

. The separation between its plates is '

d

'. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant

k_1=3

and thickness

\frac{d}{3}

while the other one has dielectric constant

\mathrm{k}_2=6

and thickness

\frac{2 \mathrm{~d}}{3}

. Capacitance of the capacitor is now A parallel plate capacitor with air between the plates has a capacitance of 9 pF . The separation between its plates is

A parallel plate capacitor with air between the plates has a capacitance of 9 pF . The separation between its plates is

Options

A $1.8 \mathrm{pF}$
B $45 \mathrm{pF}$
C $40.5 \mathrm{pF}$
D $20.25 \mathrm{pF}$

Correct answer

C. $40.5 \mathrm{pF}$

Step-by-step solution

\begin{aligned}& C^{\prime}=\frac{A \varepsilon_0}{\frac{d_1}{3}+\frac{d_2}{6}}=\frac{A \varepsilon_0}{\frac{d}{9}+\frac{2 d}{18}}=\frac{18 A \varepsilon_0}{4 d}\\ & C^{\prime}=40.5 \mathrm{PF} \end{aligned}

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