JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Capacitance

Three capacitors of capacitances

25 μ F

30 μ F

and

45 μ F

are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is

\frac{9}{x} E

. The value of

x

is ______

Answer: 86

Solution

Parallel: same voltage,

E = \frac{1}{2} (C_{1} + C_{2} + C_{3}) V^{2} = \frac{1}{2} (100 \times 1 0^{- 6}) (100)^{2} = 0.5

J.

Series:

\frac{1}{C _{s}} = \frac{1}{25} + \frac{1}{30} + \frac{1}{45} = \frac{43}{450} \Rightarrow C_{s} = \frac{450}{43} μ F .

Energy

= \frac{1}{2} C_{s} V^{2} = \frac{1}{2} (\frac{450}{43} \times 1 0^{- 6}) (100)^{2} = \frac{4.5}{43} J .

Writing this as

\frac{9}{x} E = \frac{9}{x} (0.5)

\frac{9}{x} (0.5) = \frac{4.5}{43} \Rightarrow x = 86.

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Capacitance →

More JEE Main questions on Capacitance

A capacitor $P$ with capacitance $10 \times 1 0^{- 6} F$ is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20 \times 1 0^{- 6} F$ . The char …
JEE Main 2026View solution →
The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_{1} = 2, K_{2} = 3$ , and $K_{3} = 5$ (as shown in the figure). If new capacitance is …
JEE Main 2026View solution →
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25%$ more charge from the battery. The dielectric con …
JEE Main 2026View solution →
Three parallel plate capacitors each with area A and separation d are filled with two dielectric (k₁ and k₂) in the following fashion. Which of the following is true? (k₁ > k₂)
JEE Main 2026View solution →
Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of c …
JEE Main 2026View solution →
A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates.
A sheet having thickness $(\frac{1}{3})^{rd}$ of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitan …
JEE Main 2026View solution →