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A parallel -plate capacitor having plate...

A parallel -plate capacitor having plate area `25.0cm^2` and a separation `2.00` mm between the plates .the capacitor is connected to a battery of `12.0`V.(a)find the charge on the capacitor .(b) the plate separation is decreased to `1.00`mm. Find the extra charge given by the battery to the positive plate.

Text Solution

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Here, `A = 25.0 cm^(12) = 25.0xx10^(-4) m^(2)`,
`d = 2.0 mm = 2xx10^(-3) m, V = 12 vol t`
(b) Charge on the capacitor, q = ?
`q = CV = (in_(0) A)/(d) V`
`= (8.85xx10^(-12) (25.0xx10^(-4))xx12)/(2xx10^(-3)`
`= 1.35xx10^(10)C`
(b) When plate separation is decreased to half, capacity becomes twice. The charge (q' = C'V), becomes twice. Hence extra charge given by the battery `= q' - q = 2q - q = q = 1.35xx10^(-10)C`
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