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Capacitor question

2021 · 24 Feb · Shift 1 · Q61
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  5. /2021 · 24 Feb · Shift 1 · Q61

Capacitor question

2021 · 24 Feb · Shift 1 · Q61

JEE MainPhysicsCapacitorMCQ+4 / −1
Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :
  1. A
    4 : 1
  2. B
    1 : 2
  3. C
    2 : 1
  4. D
    1 : 4
View written solutionFree

Correct answer: D

  1. Let each capacitor have capacitance CCC.

  2. Equivalent capacitance in series for two equal capacitors: 1Cs=1C+1C=2C\frac{1}{C_s} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C}Cs​1​=C1​+C1​=C2​ Cs=C2C_s = \frac{C}{2}Cs​=2C​

  3. Equivalent capacitance in parallel for two equal capacitors: Cp=C+C=2CC_p = C + C = 2CCp​=C+C=2C

  4. The ratio of equivalent capacities in the two cases (series : parallel) is Cs:Cp=C2:2CC_s : C_p = \frac{C}{2} : 2CCs​:Cp​=2C​:2C

  5. Simplify the ratio: C2:2C=1:4\frac{C}{2} : 2C = 1 : 42C​:2C=1:4

  6. Therefore, the correct option is D.

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