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A combination of parallel plate capacitors is maintained at a certain potential difference.
When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.
Let initial plate separation be $$d$$, thickness of slab $$t$$=3 mm, and increase in separation =2.4 mm.
To keep the same potential difference, the effective separation must remain unchanged:
$$d=(d+2.4)−t+\frac{t}{K}$$
$$t-\frac{t}{K}=2.4$$
$$\frac{t}{K}=t-2.4$$
$$K=\frac{t}{t-2.4}=\frac{3}{3-2.4}=\frac{3}{0.6}=5$$
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