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Question
Each of the plates shown in figure has surface area `(96/∈_0) xx 10^-12` Fm on one side and the separation between the consecutive plates is 4⋅0 mm. The emf of the battery connected is 10 volts. Find the magnitude of the charge supplied by the battery to each of the plates connected to it.
Solution
Here, three capacitors are formed and each of them has area A.
Now ,
`A = 96/∈_0 xx 10^-12 "F" - "m"`
d = 4 mm
`= 3 xx 10^-3 "m"`
The capacitance of the capacitors is given by
`C = (∈_0A)/d = (∈_0(96/∈_0) xx 10^-12)/(4 xx 10^-3)` = `24 xx 10^-9 "F"`
Because the three capacitors are arranged in series, the equivalent capacitance is given by
`C_(eq) = (24 xx 10^-9)/3 = 8 xx 10^-9 F`
The total charge on the capacitor is given by
Q = CeqV
`⇒ Q = 8 xx 10^-9 xx 10`
`⇒ Q = 8 xx 10^-8 "C"`
The charge on a single plate is given by
`Q_p = 2 xx 8 xx 10^-8`
`⇒ Q_p = 16 xx 10^-8 = 0.16 "uC"`
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