Pl ans 

Asked by jain.pradeep | 18th Feb, 2020, 08:20: PM

Expert Answer:

As shown in figure a battery of EMF E is connected a parallel plate capacitor of capacitance C through a resistance R.
 
Resistance R may be a connected resistance to control the current or resistance due to connecting wire.
 
if i is the charging current at an instant t, and q is the charge on the capacitor plates at same instant t
 
then we have , E = i R + ( q/C ) 
 
if we substitute i = dq/dt in above equation, we get ,   E = R (dq/dt) + (q/C)  ..................(1)
 
Above equation can be re arranged as  begin mathsize 14px style fraction numerator 1 over denominator R C end fraction d t space equals space fraction numerator d q over denominator E C space minus space q end fraction end style......................(2)
Using the initial condition at t = 0,  q = 0 and by integration we get the final charge Q on capacitor as
 
Q = EC [ 1 - e-t/(RC) ]  ..................(3)
 
where RC is called as time constant of the charging circuit
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when a capacitor of capacitance C is charged by a potential difference V, then charge Q = CV
 
Capacitance C of air filled parallel plate capacitor is given by, C = [ εo A ] /d
 
where A is area of plates , d is the separation distance between plates and εo is the permittivity of free space .
 
After disconnecting the potential difference, If dielectric material of dielectric constant k is introduced between parallel plates
and the separation distance d is doubled then
 
changed capacitance C' = k [ εo A ] / (2d) = (k/2) C
 
After disconnecting the potential difference which is the source of charging the capacitor, Charge Q will remain same and capacitance is changed due to chane in distance and presence of dieclectric material.
 
Hence potential difference V'  between parallel plates  is given by
 
V' = Q/C'  =  (2/k) Q/C  = (2/k) V

Answered by Thiyagarajan K | 19th Feb, 2020, 10:32: AM

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