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Question

A parallel-plate capacitor with no dielectric has a capacitance of 0.5 μF. The space between the plates is filled with equal amounts of two dielectric materials of dielectric constants 2 and 3 as shown in the figure. Find the capacitance of the system.

A
1.2 μF
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B
1.8 μF
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C
1.25 μF
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D
None of these
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Solution

The correct option is A 1.2 μF
From given we can redraw circuit as
Capacitance for upper part
C1=Kε0Ad/2=2ε0A×2d=4×0.5μF=2 μF

Capacitance for lower part
C2=Kε0Ad/2=3ε0A×2d=6×0.5μF=3 μF

Now,
1Ceq=1C1+lC2

Ceq=C1×C2C1+C2=2×32+3=65 μF=1.24 μF

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