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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.
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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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