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Question:

A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4mm. Find the dielectric constant of the slab.

3

4

6

5

Solution:

Capacitance in parallel plate capacitor is given by
C=ε₀A/d
Now introducing a slab of thickness t, the capacitance C' is
C' = ε₀A/[d' - t(1 - 1/K)]
Now q = CV
As it remains same so, C = C'
ε₀A/d = ε₀A/[d' - t(1 - 1/K)]
d = d' - t(1 - 1/K)
d = d + 2.4 × 10⁻³ - 3 × 10⁻³(1 - 1/K)
On solving we get
K = 5
Hence correct answer is B.