An air filled parallel plate capacitor initially has a capacitance of C = 9.70 n

Question

An air filled parallel plate capacitor initially has a capacitance of C = 9.70 nF.

The image given in the problem is below:
http://img191.imageshack.us/img191/3789/e25b9cadb38e349ce1beaeb.gif

Then the air gap between the plates is filled with two different dielectric materials with equal volume but with relative permittivities of ?1 = 3.83 and ?2 = 9.49 respectively. In the first case the dielectric materials are formed into two layers parallel to the plates of the capacitor. (See figure.) Determine the capacitance of the capacitor. (Note: the relative permittivity denoted by ? is equivalent to the dielectric constant denoted by ?.)

Explanation / Answer

This becomes two capacitors in parallel.

Capacitance of each such capacitor assuming it to be air-filled=2C=19.4nF

Capacitances are therefore, 19.4*3.83 and19.4*9.49=74.3nF and 184.1nF

The equivalent capacitance= 73.3*184.1/(73.3+184.1)=52.4nF

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