A parallel plate capacitor with air as medium between the plates … - Vidyadip

Question

A parallel plate capacitor with air as medium between the plates has a capacitance of $10\,\mu F$. The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant ${k_1} = 2$and ${k_2} = 4$. The capacitance of the system will now be.......$\mu F$

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Answer

(c) ${C_R} = {C_1} + {C_2} = \frac{{{k_1}{\varepsilon _0}{A_1}}}{d} + \frac{{{k_2}{\varepsilon _0}{A_2}}}{d}$
$ = \frac{{2 \times {\varepsilon _0}\frac{A}{2}}}{d} + \frac{{4 \times {\varepsilon _0}\frac{A}{2}}}{d}$$ = 2 \times \frac{{10}}{2} + 4 \times \frac{{10}}{2} = 30\,\mu F$

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