Q. 445.0( 2 Votes )

A parallel-plate capacitor having plate area 20 cm2 and separation between the plates 1.00 mm is connected to a battery of 12.0 V. The plates are pulled apart to increase the separation to 2.0 mm.

a) Calculate the charge flown through the circuit during the process.

b) How much energy is absorbed by the battery during the process?

c) Calculate the stored energy in the electric field before and after the process.

d) Using the expression for the force between the plates, find the work done by the person pulling the plates apart.

e) Show and justify that no heat is produced during this transfer of charge as the separation is increased.

Answer :


Given –


Plate area 20 cm2 = 0.002m2


Separation between the plates 1.00 mm = 0.001m


Battery Voltage = 12.0 V


We know capacitance, C


1)



Where,


A= Plate Area


d= separation between the plates,


0 = Permittivity of free space


= 8.854 × 10-12 m-3 kg-1 s4 A2


From1),


Capacitance when distance d = 0.001m, C1



Substituting values,


= 2)


When The plates are pulled apart to increase the separation to –


2.0 mm = 0.002m, then capacitance C2 becomes,



Substituting values


= 3)


From 1) and 2)


4)


We know capacitance in terms of voltage is given by –


Q = CV 5)


Where


Q= charge stored on the capacitor


C= capacitance of the capacitor


V = applied voltage


Given applied v = 12V


From 2) and 3) and 5)



=


= 6)


And



7)


a) The charge flown through the circuit during the process



From 6) and 7)



=


=


= 8)


b)Energy absorbed by the battery during the process-


We know Energy E is given by -


E=QV 9)


Where


Q = charged present on the surface


V= Applied voltage


From 8),



Applied voltage V = 12V


From 9),


Energy absorbed,



=


c)Stored energy in the electric field before and after the process


We know that stored energy in the electric field,



Before process, the energy stored -



From 2),



10)


From 3), After process, the energy stored will become



11)


d) The work done by the person pulling the plates apart.


We know, work done, W


12)


Where, f = force


d = displacement


We, know in parallel plate capacitor, the force between the plates is given by.


13)


Where, Q = charge enclosed,


σ = surface charge density,


σ, surface charge density is given by ,



From 12) and 13)


Work done,


Given, Plate area 20 cm2 = 0.002m2


Separation between the plates changed to, 2.00 mm = 0.002 m by


pulling apart.


Substituting values, from 7),






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