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Grade 12th passElectric Current

The capacitance of parallel plate capacitor is increased by a factor of 5 when a dielectric material fills the space between its plates.what is the relative permittivity of the dielectric material? If this material is placed in between the plates of a cylindrical capacitor of outer and inner raddi 12cm and 10 cm respectively, calculate the capacitance per unit length of the cylindrical capacitor.

Sri Kanth

8 Years agoGrade 12th pass

1 Answer

Eshan

8 Years ago

The capacitance of a capacitor $\propto$ relative permittivity of the dielectric material.
$C=\dfrac{\epsilon_r\epsilon_0 A}{d}$
Hence the relative permittivity of the dielectric material is 5.

The capacitance of a cyclindrical capacitor is given by
$C_{cylinder}=\dfrac{2\pi \epsilon_r\epsilon_0}{ln(\dfrac{r_2}{r_1})}$
Hence the capacitance per unit length= $\dfrac{2\pi (5)\epsilon_0}{ln(\dfrac{12}{10})}$ $=1.5nF$

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