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JEE Main 202124 FebruaryMorning Shift

Exam: JEE Main
Year: 2021
Date: 24 February
Shift: Morning Shift
Subject: Physics
Chapter: Capacitance

JEE Main 2021 · 24 February · Morning Shift · Physics · Capacitance

Two equal capacitors are first connected in series and then in...

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the

Options

A $1: 2$
B $1: 4$
C $4: 1$
D $2: 1$

Correct answer

B. $1: 4$

Step-by-step solution

For series combination,

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the

$\dfrac{1}{{C}_{e{q}_{1}}} = \dfrac{1}{C} + \dfrac{1}{C} ⇒ {C}_{e{q}_{1}} = \dfrac{C}{2}$

For parallel combination,

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the

${C}_{e{q}_{2}} = C + C ⇒ {C}_{e{q}_{2}} = 2C$

$⇒ \dfrac{{C}_{e{q}_{1}}}{{C}_{e{q}_{2}}} = \dfrac{\left(C / 2\right)}{2C} = \dfrac{1}{4} = 1: 4$

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