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Question
If the above capacitor is connected across a 6⋅0 V battery, find (a) the charge supplied by the battery, (b) the induced charge on the dielectric and (c) the net charge appearing on one of the coated surfaces.
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Solution
Given :
Capacitance of the capacitor, C = 1.42 nF
Dielectric constant, k = 4
Voltage of the battery connected, V = 6 V
(a) The charge supplied by the battery is given by
`q = CV = 1.42 xx 10^-9 xx 6`
= `8.52 xx 10^-9 "C" = 8.5 "nC"`
(b) The charge induced on the dielectric is given by
`q^' = q(1-1/K)`
= `8.52 xx 10^-9 xx (1-0.25)`
= `6.39 xx 10^-9 = 6.4 "nC"`
(c) The charge appearing on one of the coated plates is given by `Q_"net" = 8.5 - 6.4 = 2.1 "nC"`
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