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Q.

Two square plates (l×l) and dielectric (l2×l2×l) arranged as shown in figure. Find the equivalent capacitance of the structure

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a

ε0At(3K+12(K+1))

b

2ε0At(K+1K+3)

c

ε0At(K+1K+3)

d

ε0At(2K+12K+3)

answer is A.

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Detailed Solution

We can make equivalent circuit of given system in two ways as in Fig. (a) and (b). But Fig. (b) is wrong and Fig. (a) is correct Here C1=ε0A/2t/2=ε0AtC2=Kε0A/2t/2=Kε0At    and  C3=ε0A/2t=ε0A2tNow, Ceq=C1C2C1+C2+C3=ε0At[3K+12(K+1)]
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Two square plates (l×l) and dielectric (l2×l2×l) arranged as shown in figure. Find the equivalent capacitance of the structure