Three capacitors, each possessing a capacitance of 6 , are provided. The minimum and maximum capacitances that can be formed are

Correct answer: D. 2 , 18 For minimum capacitance, all three capacitors must be connected in series. (1)/(C_ ) = (1)/(C) + (1)/(C) + (1)/(C) (1)/(C_ ) = (1)/(6) + (1)/(6) + (1)/(6) = (3)/(6) = (1)/(2) C_ = 2 For maximum capacitance, all three capacitors must be connected in parallel. C_ = C + C + C C_ = 6 + 6 + 6 = 18 The minimum and maximum capacitances are 2 and 18 respectively.

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

Three capacitors, each possessing a capacitance of 6 , are...

Three capacitors, each possessing a capacitance of

6 \mu\text{F}

, are provided. The minimum and maximum capacitances that can be formed are

Options

A $3 \mu\text{F}$ , $12 \mu\text{F}$
B $6 \mu\text{F}$ , $18 \mu\text{F}$
C $2 \mu\text{F}$ , $12 \mu\text{F}$
D $2 \mu\text{F}$ , $18 \mu\text{F}$

Correct answer

D. $2 \mu\text{F}$ , $18 \mu\text{F}$

Step-by-step solution

For minimum capacitance, all three capacitors must be connected in series.

\dfrac{1}{C_\min} = \dfrac{1}{C} + \dfrac{1}{C} + \dfrac{1}{C}

\dfrac{1}{C_\min} = \dfrac{1}{6} + \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{3}{6} = \dfrac{1}{2}

C_\min = 2 \mu\text{F}

For maximum capacitance, all three capacitors must be connected in parallel.

C_\max = C + C + C

C_\max = 6 + 6 + 6 = 18 \mu\text{F}

The minimum and maximum capacitances are

2 \mu\text{F}

and

18 \mu\text{F}

respectively.

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