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

Q 1 :

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 _______ . [2024]

(86) In series combination: $C_{1} = 25 + 30 + 45 = 100 μ F$

In parallel combination: $\frac{1}{C_{2}} = \frac{1}{25} + \frac{1}{30} + \frac{1}{45} \Rightarrow C_{2} = \frac{450}{43} μ F$

Energy $E = \frac{1}{2} C V^{2}$

$\frac{E_{2}}{E_{1}} = \frac{C_{2}}{C_{1}} = \frac{450 / 43}{100} = \frac{9}{86} \Rightarrow E_{2} = \frac{9}{86} E$

$\Rightarrow \frac{9}{86} E = \frac{9}{x} E \Rightarrow x = 86$

Q 2 :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is: [2024]

$\frac{11 ϵ_{0} A}{18 d}$
$\frac{13 ϵ_{0} A}{17 d}$
$\frac{11 ϵ_{0} A}{20 d}$
$\frac{18 ϵ_{0} A}{11 d}$

1

2

3

4

(1)

All capacitors are in parallel combination.

Also, effective area is common area only

$C_{e q} = C_{1} + C_{2} + C_{3}$

$= \frac{ϵ_{0} A}{3 \times d} + \frac{ϵ_{0} A}{3 \times 2 d} + \frac{ϵ_{0} A}{3 \times 3 d}$

$= \frac{6 ϵ_{0} A + 3 ϵ_{0} A + 2 ϵ_{0} A}{18 d} = \frac{11 ϵ_{0} A}{18 d}$

Q 3 :

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is [2024].

$\frac{1}{4} C V^{2}$
$2 C V^{2}$
$\frac{1}{2} C V^{2}$
$\frac{3}{4} C V^{2}$

1

2

3

4

(1)

Initial energy $= \frac{1}{2} C V^{2} + \frac{1}{2} C \times 4 V^{2} = \frac{5 C V^{2}}{2}$

$\frac{2 C V - q}{C} = \frac{C V + q}{C}$

$2 C V - C V = 2 q$

$q = \frac{C V}{2}$

Final charge on capacitor $= \frac{3 C V}{2}$

$E n e r g y_{final} = 2 \times {(\frac{3 C V}{2})}^{2} \times \frac{1}{2 C} = \frac{9 C V^{2}}{4}$

Decrease in Energy $= \frac{5 C V^{2}}{2} - \frac{9 C V^{2}}{4} = \frac{C V^{2}}{4}$

Q 4 :

A $16 Ω$ wire is bent to form a square loop. A 9V battery with internal resistance $1 Ω$ is connected across one of its sides. If a $4 μ F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $x / 2$ $μ J$ , where $x$ = ______. [2024]

(81)

At steady state, the current supplied from the battery,

$I = \frac{V}{R_{eq}} = \frac{9}{1 + \frac{12 \times 4}{12 + 4}} = \frac{9}{4} A$

$I_{1} = \frac{9}{4} \times \frac{4}{16} = \frac{9}{16} A$

$V_{A} - V_{B} = I_{1} \times 8 = \frac{9}{16} \times 8 = \frac{9}{2} V$

$∴$ $U = \frac{1}{2} \times 4 \times \frac{81}{4} μ J = \frac{81}{2} μ J$

$∴$ $x = 81$

Q 5 :

Two capacitors $C_{1}$ and $C_{2}$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_{1}$ and $U_{2}$ , respectively. Which of the given statements is true? [2025]

$C_{1} > C_{2}, U_{1} > U_{2}$
$C_{2} > C_{1}, U_{2} > U_{1}$
$C_{1} > C_{2}, U_{1} < U_{2}$
$C_{2} > C_{1}, U_{2} < U_{1}$

1

2

3

4

(2)

For a capacitor at steady state

q = CV and $U = \frac{1}{2} C V^{2}$

Since $C_{1}$ and $C_{2}$ are connected in parallel, $V_{1} = V_{2}$

Also from graph $q_{1} < q_{2}$

$\Rightarrow C_{1} V_{1} < C_{2} V_{2}$

i.e., $C_{1} < C_{2}$ or $C_{2} > C_{1}$

$\frac{U_{1}}{U_{2}} = \frac{C_{1} V_{1}^{2}}{C_{2} V_{2}^{2}} = \frac{C_{1}}{C_{2}} < 1$

or $U_{1} < U_{2}$ or $U_{2} > U_{1}$

Q 6 :

A capacitor, $C_{1} = 6 μ F$ is charged to a potential difference of $V_{0} =$ 5 V using a 5 V battery. The battery is removed and another capacitor, $C_{2} = 12 μ F$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ( $q_{1}$ and $q_{2}$ ) on the capacitors $C_{1}$ and $C_{2}$ when equilibrium condition is reached? [2025]

$q_{1} = 15 μ C, q_{2} = 30 μ C$
$q_{1} = 30 μ C, q_{2} = 15 μ C$
$q_{1} = 10 μ C, q_{2} = 20 μ C$
$q_{1} = 20 μ C, q_{2} = 10 μ C$

1

2

3

4

(3)

Initially

Finally

q_{1}^{'} = 6 \times 5 = 30 μ C

$6 V_{C} + 12 V_{C} = 30 + 0$

$18 V_{C} = 30$

$\Rightarrow V_{C} = \frac{30}{18} = \frac{5}{3} Volt$

$\Rightarrow q_{1} = \frac{6 \times 5}{3} = 10 μ C$

and $q_{2} = \frac{12 \times 5}{3} = 20 μ C$

Q 7 :

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is (in pF) [2025]

600
200
400
100

1

2

3

4

(2)

New potential $= \frac{C_{0} V_{0}}{C_{0} + C} = \frac{V_{0}}{3}$

$3 C_{0} V_{0} = C_{0} V_{0} + C V_{0}$

$2 C_{0} V_{0} = C V_{0}$

$C = 2 C_{0} = 2 \times 100 = 200 pF$

Q 8 :

Four capacitors each of capacitance 16 $μ$ F are connected as shown in the figure. The capacitance between points A and B is : ______ (in $μ$ F). [2025]

(64)

$C_{eq} = 4 C = 64$

Q 9 :

Space between the plates of a parallel plate capacitor of plate area 4 ${cm}^{2}$ and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ______ pF. (Given $ε_{0} = 8.85 \times 10^{- 12} F / m$ ) [2025]

(15)

$\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} = \frac{d / 2}{A k_{1} ε_{0}} + \frac{d / 2}{A k_{2} ε_{0}}$

$= (\frac{1}{k_{1}} + \frac{1}{k_{2}}) \frac{d}{2 A ε_{0}} = (\frac{1}{3} + \frac{1}{5}) \frac{d}{2 A ε_{0}}$

$\frac{1}{C} = \frac{4}{15} \frac{d}{A ε_{0}}$

$C = \frac{15}{4} \times \frac{A ε_{0}}{d}$

$= \frac{15}{4} \times \frac{4 \times 10^{- 4} \times 8.85 \times 10^{- 12}}{1.77 \times 10^{- 3}} = 7.5 p F$

Finally equivalent capacitance ( $C_{eq}$ ) = 7.5 + 7.5 = 15 pF

Q 10 :

The equivalent capacitance of the combination shown is [2023]

$\frac{C}{2}$
$4 C$
$2 C$
$\frac{5}{3} C$

1

2

3

4

(3)

The circuit can be reduced to

$Parallel combination C_{eq} = C + C = 2 C$

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

1

2

3

4

(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]

(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]

(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]

(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]

(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]

(8)

$C_{1} = \frac{5 ε_{0} (A / 2)}{d / 2} = \frac{5 ε_{0} A}{d} = 5 C$

$C_{2} = \frac{2 ε_{0} (A / 2)}{d / 2} = \frac{2 ε_{0} A}{d} = 2 C$

$C_{1}$ and $C_{2}$ in series

$C' = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{(5 C) (2 C)}{7 C} = \frac{10}{7} C$

$C_{3} = \frac{3 ε_{0} (A / 2)}{d / 2} = 3 C$

$C_{4} = \frac{2 ε_{0} (A / 2)}{d / 2} = 2 C$

$C_{4}$ and $C_{3}$ in series; $C'' = \frac{(2 C) (3 C)}{5 C} = \frac{6}{5} C$

$C'$ and $C''$ in parallel;

So, $C_{eq} = C (\frac{6}{5} + \frac{10}{7}) = C (\frac{42 + 50}{35}) = \frac{92}{35} C$

$\frac{92}{35} C = \frac{n C}{3}$

$n = \frac{92 \times 3}{35} = 7.9 \approx 8$

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]

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

1

2

3

4

(1)

$For C_{A} :$

$Let \frac{ε_{0} A}{d} = C$

$∴$ $C_{A} = \frac{K_{1} C}{2} + \frac{K_{1} K_{2} C}{K_{1} + K_{2}}$

$= K_{1} C [\frac{K_{1} + 2 K_{2}}{2 (K_{1} + K_{2})}]$

$For C_{B} :$

$C_{B} = \frac{K_{2} C}{2} + \frac{K_{1} K_{2} C}{K_{1} + K_{2}}$

$= K_{2} C [\frac{K_{1} + 2 K_{2}}{2 (K_{1} + K_{2})}]$

$For C_{C} :$

$C_{C} = \frac{2 K_{1} K_{2} C}{K_{1} + K_{2}}$

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

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]

(4)

$V = \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}} = \frac{10^{- 5} \times 6 + 0}{3 \times 10^{- 5}}$

$V = 2 volt$

$Q_{2} = C_{2} V = 2 \times 10^{- 5} \times 2 = 4 \times 10^{- 5} C$

Topic Question Set

Q 2 :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is: [2024]

Q 3 :

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is [2024].

Q 4 :

A $16 Ω$ wire is bent to form a square loop. A 9V battery with internal resistance $1 Ω$ is connected across one of its sides. If a $4 μ F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $x / 2$ $μ J$ , where $x$ = ______. [2024]

Q 5 :

Two capacitors $C_{1}$ and $C_{2}$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_{1}$ and $U_{2}$ , respectively. Which of the given statements is true? [2025]

Q 7 :

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is (in pF) [2025]

Q 8 :

Four capacitors each of capacitance 16 $μ$ F are connected as shown in the figure. The capacitance between points A and B is : ______ (in $μ$ F). [2025]

Q 10 :

The equivalent capacitance of the combination shown is [2023]

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]

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]

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]

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]

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 1 : Three capacitors of capacitances 25 μF, 30 μF, and 45 μF 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 9xE. The value of x is _______ . [2024]

Q 2 : A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is A3 and the height is d, the capacitance of the arrangement is: [2024]

Q 3 : Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is [2024].

Q 4 : A 16Ω wire is bent to form a square loop. A 9V battery with internal resistance 1Ω is connected across one of its sides. If a 4μF capacitor is connected across one of its diagonals, the energy stored by the capacitor will be x/2 μJ, where x = ______. [2024]

Q 5 : Two capacitors C1 and C2 are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U1 and U2, respectively. Which of the given statements is true? [2025]

Q 7 : Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is (in pF) [2025]

Q 8 : Four capacitors each of capacitance 16 μF are connected as shown in the figure. The capacitance between points A and B is : ______ (in μF). [2025]

Q 10 : The equivalent capacitance of the combination shown is [2023]

Q 11 : A parallel plate capacitor of capacitance 2F is charged to a potential V. The energy stored in the capacitor is E1. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E2. The ratio E2/E1 is [2023]

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 __________μJ [2023]

Q 14 : In the given circuit, C1=2 μF, C2=0.2 μF, C3=2 μF, C4=4 μF, C5=2 μF, C6=2 μF, the charge stored on capacitor C4 is ______ μC. [2023]

Q 15 : In the given figure, the total charge stored in the combination of capacitors is 100 μC. The value of 'x' is _________ . [2023]

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 K1=2, K2=3, and K3=5 (as shown in the figure). If the new capacitance is n3C, then the value of n is _______. [2026]

Q 17 : Three parallel plate capacitors each with area A and separation d are filled with two dielectrics (k1 and k2) in the following fashion. Which of the following is true? (k1>k2) [2026]

Want Us to Email you About Special Offers & Updates?

Q 2 :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is: [2024]

Q 3 :

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is [2024].

Q 4 :

A $16 Ω$ wire is bent to form a square loop. A 9V battery with internal resistance $1 Ω$ is connected across one of its sides. If a $4 μ F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $x / 2$ $μ J$ , where $x$ = ______. [2024]

Q 5 :

Two capacitors $C_{1}$ and $C_{2}$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_{1}$ and $U_{2}$ , respectively. Which of the given statements is true? [2025]

Q 7 :

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is (in pF) [2025]

Q 8 :

Four capacitors each of capacitance 16 $μ$ F are connected as shown in the figure. The capacitance between points A and B is : ______ (in $μ$ F). [2025]

Q 10 :

The equivalent capacitance of the combination shown is [2023]

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]

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]

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]

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]