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A parallel plate capacitor has plate are...

A parallel plate capacitor has plate area `A = 2 xx 10^(-4) m^(2)`.The separation between the plates is `d = 10^(-3) m`. If `K_(1) =2` and `K_2 =4` are the dielectric constants, find the capacity of the condenser.

Text Solution

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Here, capacitor is assumed to have two capacitors in series as shown in the figure below.

Here, `C_(1) = (epsilon_(0)K_(1)A)/(d//2) = 2 (epsilon_(0)K_(1)A)/d`
`C_(2) = (epsilon_(0)K_(2)A)/(d//2) = 2 (epsilon_(0)K_(2)A)/d`
If C is the total capacity of the capacitor then,
`1/C = 1/C_(1) + 1/C_(2)`
`1/C = d/(2epsilon_(0)K_(1)A) + d/(2epsilon_(0)K_(2)A)`
`1/C = d/(2epsilon_(0)A) ((K_(1)+ K_(2))/(K_(1)K_(2)))`
`rArr = (2 xx 8.85 xx 10^(-12) xx 2 xx 10^(-4) xx 2 xx 4)/(10^(-3) (2 + 4))`
`=4.72 xx 10^(-12) F`
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