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The capacitance of a capacitor between 4...

The capacitance of a capacitor between` 4//3` times its original value if a dielectric slab of thickness `t=d//2` is inserted between the plates (d is the separation between the plates). What is the dielectric consant of the slab?

A

8

B

4

C

6

D

2

Text Solution

Verified by Experts

The correct Answer is:
d
In air , `C=(epsilon_(0)A)/(d),` with slab , `C.=(epsilon_(0)A)/((d-t+(t)/(K)))`
Since `C.=(4C)/(3)rArr(epsilon_(0)A)/((d-t+(t)/(K)))=(4)/(3)*(epsilon_(0)A)/(d)` `rArr3d=4(d-t+(t)/(K))=4(d-(d)/(2)+(d)/(2K))=(4d)/(2)(1+(1)/(K))`
`rArr3=2(1+(1)/(K))rArr3=2+(2)/(K)rArr1=(2)/(K)rArrK=2`
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