Electric Potential and Capacitance | Physics JEE previous year questions with Solutions

Q 11 :

A parallel plate capacitor of capacitance $2 F$ is charged to a potential $V$ . The energy stored in the capacitor is $E_{1}$ . The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_{2}$ . The ratio $E_{2} / E_{1}$ is [2023]

2 : 1
1 : 2
1 : 4
2 : 3

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(2)

Initially,

$Q_{1} = C V = (2) V$

$E_{1} = \frac{1}{2} C V^{2} = \frac{1}{2} (2) V^{2} = V^{2}$

Finally,

Charge on each capacitor,

$Q_{2} = \frac{Q_{1}}{2} = \frac{2 V}{2} = V$

$E_{2} = 2 (\frac{1}{2} \frac{Q_{2}^{2}}{C}) = \frac{V^{2}}{2}$

$∴$ $\frac{E_{2}}{E_{1}} = \frac{1}{2}$

Q 12 :

A capacitor of capacitance $900 μ F$ is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of the uncharged capacitor is connected to the positive plate and the other plate of the uncharged capacitor is connected to the negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{- 2}$ J. The value of $x$ is ________ . [2023]

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(225)

$C = 900 μ F$

$Hence Q = C V = 900 \times 10^{- 6} \times 100 = 9 \times 10^{- 2} = 90 mC$

Common potential will be developed across both capacitors by KVL.

Total charge on left plates of capacitors should be conserved.

$∴$ $90 mC + 0 = 2 C V_{0}$

$C V_{0} = 45 mC$

$Heat dissipated = U_{i} - U_{f}$ [Change in energy stored in the capacitors]

$= \frac{1}{2} \frac{{(90 mC)}^{2}}{900 μ F} - 2 \times \frac{1}{2} \frac{{(45 mC)}^{2}}{900 μ F} [U = \frac{Q^{2}}{2 C}]$

$= \frac{1}{2 \times 900 \times 10^{- 6}} (8100 - 4050) \times 10^{- 6} = 2.25 Joule$

Q 13 :

A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is __________ $μ J$ [2023]

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(6)

$Q = C V = 600 \times 10^{- 12} \times 200 = 12 \times 10^{- 8} C$

$Initial energy = \frac{1}{2} C V^{2}$

$= \frac{1}{2} \times 600 \times 10^{- 12} \times {(200)}^{2} = 12 μ J$

When connected to another uncharged capacitor

charge will be equally distributed on identical capacitors

$Q' = \frac{Q}{2} = 6 \times 10^{- 8}$

$Final energy = 2 \times \frac{Q'^{2}}{2 C} = \frac{Q'^{2}}{C}$

$= \frac{{(6 \times 10^{- 8})}^{2}}{600 \times 10^{- 12}} = 6 μ J$

$Energy lost = Initial energy - Final energy$

$= (12 - 6) μ J = 6 μ J$

Q 14 :

In the given circuit, $C_{1} = 2 μ F, C_{2} = 0.2 μ F, C_{3} = 2 μ F,$ $C_{4} = 4 μ F, C_{5} = 2 μ F, C_{6} = 2 μ F,$ the charge stored on capacitor $C_{4}$ is ______ $μ C$ . [2023]

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(4)

$C_{eq} = 0.5 μ F$

$Q = 0.5 \times 10 = 5 μ C$

$Q' = \frac{5 μ C \times 0.8}{0.8 + 0.2} = 4 μ C$

Q 15 :

In the given figure, the total charge stored in the combination of capacitors is $100 μ C$ . The value of $' x'$ is _________ . [2023]

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(5)

$Charge on C_{1} is Q_{1} = 2 \times 10 = 20 μ C$ ...(i)

$Charge on C_{2} is Q_{2} = x \times 10 = 10 x μ C$ ...(ii)

$Charge on C_{3} is Q_{3} = 3 \times 10 = 30 μ C$ ...(iii)

$Total charge = 20 + 10 x + 30 = 100$

$\Rightarrow x = 5$

Q 16 :

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 the new capacitance is $\frac{n}{3} C$ , then the value of $n$ is _______. [2026]

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(8)

Q 17 :

Three parallel plate capacitors each with area A and separation d are filled with two dielectrics $(k_{1} and k_{2})$ in the following fashion. Which of the following is true? $(k_{1} > k_{2})$ [2026]

$C_{A} > C_{C} > C_{B}$
$C_{C} > C_{A} > C_{B}$
$C_{B} > C_{C} > C_{A}$
$C_{C} > C_{B} > C_{A}$

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(1)

Q 18 :

A capacitor P with capacitance $10 \times 10^{- 6} F$ 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 $20 \times 10^{- 6} F$ . The charge on capacitor Q when equilibrium is established will be $α \times 10^{- 5} C$ .

(assume capacitor Q does not have any charge initially), the value of $α$ is __________. [2026]

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Topic Question Set

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Q 13 :

A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is __________ $μ J$ [2023]

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Q 14 :

In the given circuit, $C_{1} = 2 μ F, C_{2} = 0.2 μ F, C_{3} = 2 μ F,$ $C_{4} = 4 μ F, C_{5} = 2 μ F, C_{6} = 2 μ F,$ the charge stored on capacitor $C_{4}$ is ______ $μ C$ . [2023]

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Q 15 :

In the given figure, the total charge stored in the combination of capacitors is $100 μ C$ . The value of $' x'$ is _________ . [2023]

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Q 17 :

Three parallel plate capacitors each with area A and separation d are filled with two dielectrics $(k_{1} and k_{2})$ in the following fashion. Which of the following is true? $(k_{1} > k_{2})$ [2026]

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