QJEEAdv18Phafb9: JEE Advanced 2018 Physics - Class 12 JEEAdv18Phafb9 Solution: Three identical capacitors and have a capacitance of each and…

Question

Verified Solution • 2025–26 Session moderate

Three identical capacitors

{C_1},{C_2}

and

{C_3}

have a capacitance of

1.0\,\mu F

each and they are unchanged 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

{\varepsilon _r}.

The cell electromotive force

\left( {emf} \right)\,\,{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\,\mu C.

The value of

{\varepsilon _r} =

_________________.

JEE Advanced 2018 Paper 1 Offline Physics - Capacitor Question 13 English

Accepted Answer

Given C₁ = C₂ = C₃ = 1.0 $\mu$ F and V₀ = 8 V

When S₁ is close and S₂ is open. Charge on C₃ is 8 $\mu$ C.

The circuit is

JEE Advanced 2018 Paper 1 Offline Physics - Capacitor Question 13 English Explanation 1

When S₁ is open and S₂ is close. Charge on C₃ is 5 $\mu$ C. Therefore, charge on C₁ and C₂ will be 3 $\mu$ C.

JEE Advanced 2018 Paper 1 Offline Physics - Capacitor Question 13 English Explanation 2

The potential difference across C₃ is equal to the potential difference across C₁ and C₂ together i.e.,

${{{q_1}} \over {C{'_1}}} + {{{q_2}} \over {{C_2}}} = {{{q_3}} \over {{C_3}}}$ ,

${{3\mu C} \over {{ \in _r}(1\mu F)}} + {{3\mu C} \over {1\mu F}} = {{5\mu C} \over {1\mu F}}$ .

Solve to get ${ \in _r} = 1.5$ .

Step-by-Step Verified Solution