A parallel plate capacitor of area ' A ' plate separation ' d ' is...

A parallel plate capacitor of area '

A

' plate separation '

d

' is filled with two dielectrics as shown. What is the capacitance of the arrangement? A parallel plate capacitor of area ' A ' plate separation ' d ' is filled with two dielectrics as shown. What is the

A parallel plate capacitor of area ' A ' plate separation ' d ' is filled with two dielectrics as shown. What is the

Options

A $\frac{3 K \varepsilon_{0} A}{4 d}$
B $\frac{4 K \varepsilon_{0} A}{3 d}$
C $\frac{(K+1) \varepsilon_{0} A}{2 d}$
D $\frac{K(K+3) \varepsilon_{0} A}{2(K+1) d}$

Correct answer

D. $\frac{K(K+3) \varepsilon_{0} A}{2(K+1) d}$

Step-by-step solution

c_{1}=

\frac{(A / 2) \varepsilon_{0}}{d / 2}=\frac{A \varepsilon_{0}}{d},

c_{2}=K

\frac{A \varepsilon_{0}}{d},

c_{3}=K

\frac{A \varepsilon_{0}}{2 d}<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fbitsat%252F-2J2c5Qbdiu4RPjNxqVYEm9IxIFFFQQ25PfTCZIJjOo.original.fullsize.png%3Falt%3Dmedia \text{ and } clean=1 \text{ and } v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2F-2J2c5Qbdiu4RPjNxqVYEm9IxIFFFQQ25PfTCZIJjOo.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2F-2J2c5Qbdiu4RPjNxqVYEm9IxIFFFQQ25PfTCZIJjOo.original.fullsize.png?alt=media"> \\ \therefore \quad c_{e q.}=\frac{c_{1} \times c_{2}}{c_{1}+c_{2}}+

c_{3}=

\frac{(3+\mathrm{K}) \mathrm{K} A \varepsilon_{0}}{2 d(\mathrm{ K}+1)}\left(\because C_{1}\right.

and

C_{2}

are in series and resultant of these two in parallel with

C_{3}

)

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