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Q.

The space between the plates of two parallel plate capacitors is filled by two dielectric slabs having dielectric constants k1 and k2 as shown in fig-(1) and (2). Plate area of each capacitor is A and plate separation is d. If c1 and c2  be the capacitances of the capacitors in arrangements (1) and (2) respectively, then c1c2 is

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a

k1+k22k1k2

b

k1k2k1+k2

c

2k1k2k1+k22

d

k1+k224k1k2

answer is D.

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Detailed Solution

c1=ε0k1A/2d+ε0k2A/2d=ε0k1+k2A2d1c2=d/2k1ε0A+d/2k2ε0A=d2ε0Axk1+k2k1k2⇒c2=2ε0Adk1k2k1+k2∴c1c2=ε0(k1+k2)A2dxdk1+k22ε0Ak1k2=k1+k224k1k2
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