Question

two capacitor are connected in series across2kv line the energy stored in the system is 2.4j if the same capacitor connected in parallel across the same line the energy stored is 10j find individual capacitors​

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PHYSICS

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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VIDEO EXPLANATION

ANSWER

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

μF

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