The potential difference between a pair of oppositely chargedparallel plates is

Question

The potential difference between a pair of oppositely chargedparallel plates is 376 V. (a) If the spacing between the plates is doubled without altering the charge on theplates, what is the new potential difference between theplates?
V
(b) If the plate spacing is tripled while the potential differencebetween the plates is kept constant, what is the ratio of the finalcharge on one of the plates to the original charge?
(Qfinal / Qinitial) (a) If the spacing between the plates is doubled without altering the charge on theplates, what is the new potential difference between theplates?
V
(b) If the plate spacing is tripled while the potential differencebetween the plates is kept constant, what is the ratio of the finalcharge on one of the plates to the original charge?
(Qfinal / Qinitial)

Explanation / Answer

The potential difference between a pair of oppositely chargedparallel plates is V = 376 V
(a) If the spacing between the plates is doubled without altering the charge on theplates then capacity is half
Since C = A / d
         C 1/d
( C ' /C ) = ( d / d')
               = ( d / 2d )
               = 1/ 2
           C ' = 0.5 C
The new potential difference between the plates V ' = Q / C '
                                                                             = Q / ( 0.5 C )
                                                                             = 2Q /C
                                                                             = 2V
                                                                             = 2*376 Volt
                                                                             = 752 Volt

(b) The plate spacing is tripled while the potential differencebetween the plates is kept constant.
Capacity C ' /C = d / d'
                        = d / 3d = 1/ 3
                 C ' = C / 3

potential difference is constant .
New charge Q ' = C ' V
                        = ( C / 3 ) V
                        = (CV / 3 )
                        = Q / 3
the ratio of the final charge on one of the plates to the originalcharge Q ' / Q = 1/3

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