First slide
Capacitance
Question

The space between the plates of a parallel plate capacitor is filled completely with a dielectric substance having dielectric constant 4 and thickness 3 mm and its capacitance is C. The distance between the plates in now increased by inserting a second sheet of thickness 5 mm and dielectric constant K. If the capacitance of the capacitor so formed is C/2 then  the value of K is

Moderate
Solution

Original capacitance 4C
Final capacitance
4C×3KC54C+3KC5=4C2
Solving K = 20/3

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