Question

When two capacitors are connected in series and connected across 4 kV line, the energy stored in the system is 8 J. the same capacitors, if connected in parallel across the same line, the energy stored is 36 J. Find the individual capacitances.




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Answer 1

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here, is your ⇒solution for the prob

Answer 2

Explanation:

Let the capacitance of two capacitors be C

1

and C

2

.

Line voltage V=4000 volts

Parallel connection :

Equivalent capacitance of series connection C

p

=C

1

+C

2

Energy stored E

p

=

2

1

C

p

V

2

∴ 36=

2

1

(C

1

+C

2

)(4000)

2

⟹ C

1

+C

2

=4.5μF

We get C

2

=4.5μF−C

1

Series connection :

Equivalent capacitance of series connection C

s

=

C

1

+C

2

C

1

C

2

=

4.5

C

1

C

2

Energy stored E

s

=

2

1

C

s

V

2

∴ 8=

2

1

(

4.5

C

1

C

2

)(4000)

2

⟹ C

1

C

2

=4.5μF

Or C

1

(4.5−C

1

)=4.5

Or C

1

2

−4.5C

1

+4.5=0

Solving we get C

1

=1.5μF

⟹ C

2

=4.5−1.5=3.0μF

hope it's helpful to you ✨