Three identical capacitors C 1 , C 2 and C 3 have a capacitance of 1.0 µF each and they are uncharged initially. They are connected in a circuit as shown in the figure and C 1 is then filled completely with a dielectric material of relative permittivity ε r . The cell electromotive force (emf) V 0 = 8V. First the switch S 1 is closed while the switch S 2 is kept open. When the capacitor C 3 is fully charged, S 1 is opened and S 2 is closed simultaneously. When all the capacitors reach equilibrium, the charge on C 3 is found to be 5 µC. The value of ε r =____________.

Text Solution
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(1.50)
Sol.


= 0, 
5 =
, 8C – q = 5C
= 3
,
⇒ q = 3C
= 1 + 
⇒
= 
ε r =
= 1.5
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