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Please help! Figure shows charge (q) versus voltage (V) graph for series and parallel combinationof two given capacitors. The capacitances are:

Figure shows charge (q) versus voltage (V) graph for series and parallel combination

of two given capacitors. The capacitances are:

  • Option 1)

    40\mu F\: \: and\: \: 10\mu F

  • Option 2)

    60\mu F\: \: and\: \: 40\mu F

  • Option 3)

    50\mu F\: \: and\: \: 30\mu F

  • Option 4)

    20\mu F\: \: and\: \: 30\mu F

 
Answers (1)
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Series Grouping -

\frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\cdots

- wherein

 

 

Parallel Grouping -

C_{eq}=C_{1}+C_{2}+\cdots

- wherein

 

 

For parallel 

C_{eq}=C_1+C_2

So, q_{1}= 10 (C_1+C_2)=500\mu C

=>C_1+C_2=50\mu C............(1)

For series

C_{eq}=\frac{C_1C_2}{C_1+C_2}

q_2=10C_{eq}=80

So,

10\times \frac{C_1C_2}{C_1+C_2}=80

10\times \frac{C_1C_2}{50}=80

C_1 C_2=400

C_2=10\mu F

C_1=40\mu F


Option 1)

40\mu F\: \: and\: \: 10\mu F

Option 2)

60\mu F\: \: and\: \: 40\mu F

Option 3)

50\mu F\: \: and\: \: 30\mu F

Option 4)

20\mu F\: \: and\: \: 30\mu F

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