A) \[\frac{3K}{K+3}\]
B) \[\frac{3}{4}K\]
C) \[\frac{4K}{K+3}K\]
D) \[\frac{4}{3}K\]
Correct Answer: C
Solution :
The capacitance of a parallel plate capacitor in the absence of the dielectric is \[{{C}_{0}}=\frac{{{\varepsilon }_{0}}A}{d}\] If a dielectric slab is partially filled between the plates of capacitor \[C=\frac{{{\varepsilon }_{0}}A}{d-t+\frac{t}{K}}\] \[C=\frac{{{\varepsilon }_{0}}A}{\left( d-\frac{3}{4}d \right)+\left( \frac{3d}{4K} \right)}\] \[C=\frac{{{\varepsilon }_{0}}A}{\frac{d}{4}+\frac{3d}{4K}}\] \[=\frac{4K{{\varepsilon }_{0}}A}{d(K+3)}\] \[\therefore \] \[\frac{C}{{{C}_{0}}}=\frac{4K{{\varepsilon }_{0}}A}{d(K+3)}\times \frac{d}{{{\varepsilon }_{0}}A}\] \[=\frac{4K}{(K+3)}\]You need to login to perform this action.
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