Effective capacitance of parallel combination of two capacitors C _ 1 and C _ 2 is 10 . When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor C _ 2 is 4 times

Correct answer: C. 1.6 Given C _ 1 + C _ 2 = 10 ...(i) 4((1)/(2) C _ 1 V ^ 2 ) = (1)/(2) C _ 2 V ^ 2 ⇒ 4 C _ 1 = C _ 2 ...(ii) From equation (i) and (ii) C _ 1 = 2 C _ 2 = 8 If they are in series C _ eq = C _ 1 C _ 2 C _ 1 + _ 2 = 1.6

JEE Main 20208 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 8 January
Shift: Morning Shift
Subject: Physics
Chapter: Capacitance

JEE Main 2020 · 8 January · Morning Shift · Physics · Capacitance

Effective capacitance of parallel combination of two capacitors C _...

Effective capacitance of parallel combination of two capacitors

{C}_{1}

and

{C}_{2}

10\muF .

When these capacitors are individually connected to a voltage source of

1V,

the energy stored in the capacitor

{C}_{2}

4

times that of

{C}_{1} .

If these capacitors are connected in series, their effective capacitance will be: Effective capacitance of parallel combination of two capacitors C _ 1 and C _ 2 is 10 . When these capacitors are

Effective capacitance of parallel combination of two capacitors C _ 1 and C _ 2 is 10 . When these capacitors are

Options

A $4.2\muF$
B $3.2\muF$
C $1.6\muF$
D $8.4\muF$

Correct answer

C. $1.6\muF$

Step-by-step solution

Given

{C}_{1} + {C}_{2} = 10\muF

...(i)

4\left(\dfrac{1}{2}{C}_{1}{V}^{2}\right) = \dfrac{1}{2}{C}_{2}{V}^{2}

⇒ 4{C}_{1} = {C}_{2}

...(ii)
From equation (i) and (ii)

{C}_{1} = 2\muF

{C}_{2} = 8\muF

If they are in series

{C}_{eq} = \dfrac{{C}_{1}{C}_{2}}{{C}_{1}{+}_{2}} = 1.6\muF

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