# 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. Option 1) 3 Option 2) 4 Option 3) 5 Option 4) 6

N neha
D Divya Saini

As we learnt in

Parallel Grouping -

$\dpi{100} C_{eq}=C_{1}+C_{2}+\cdots$

- wherein

Parallel Grouping -

$\dpi{100} C_{eq}=C_{1}+C_{2}+\cdots$

- wherein

$C_{before}= \frac{E_{0}A}{3} \, \, \, \, \, \, -(i)$

$C_{after}= \frac{k\frac{\epsilon_{0}A}{3} \ \frac{\epsilon_{0}A}{2.4}}{k\frac{\epsilon_{0}A}{3}+ \frac{\epsilon_{0}A}{2.4}}\, \, \, \, \, \, -(ii)$

$\therefore Equation (i) and (ii)$

$\frac{\epsilon_{0}4}{3}= \frac{k\frac{\epsilon_{0}A}{3} \ \frac{\epsilon_{0}A}{2.4}}{k\frac{\epsilon_{0}A}{3}+ \frac{\epsilon_{0}A}{2.4}}\, \, \, \, \, \,$

$\Rightarrow \, 3k= 2.4k + 3\, \, \, \, \, \, \, or \, \, \, \, \, \, 0.6k=3$

$\therefore k = \frac{3}{0.6}\, \, \, \, \, \, , k= 5$

Option 1)

3

Incorrect Option

Option 2)

4

Incorrect Option

Option 3)

5

Correct Option

Option 4)

6

Incorrect Option

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