Q. No.A sphere of capacitance \(100~\text{pF}\) is charged to a potential of \(100~\text{V}.\) Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is \(\alpha \times 10^{-7} ~\text{J} .\) The value of \(\alpha\) is:
(combined capacitance of spheres is \(200~\text{pF}\))
1. \(5\)
2. \(\dfrac{5}{2}\)
3. \(\dfrac{7}{2}\)
4. \(\dfrac{9}{2}\)
(combined capacitance of spheres is \(200~\text{pF}\))
1. \(5\)
2. \(\dfrac{5}{2}\)
3. \(\dfrac{7}{2}\)
4. \(\dfrac{9}{2}\)
Subtopic: Energy stored in Capacitor |
79%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(V\) \(x\)
1. \(-2\)
2. \(1\)
3. \(-1\)
4. \(2\)
1. \(-2\)
2. \(1\)
3. \(-1\)
4. \(2\)
Subtopic: Energy stored in Capacitor |
57%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
A parallel plate capacitor of capacitance \(1~\mu F\) is charged to a potential difference of \(20~\text V\). The distance between plates is \(1 \mu \text{m}\). The energy density between plates of capacitor is.
1. \(1.8 \times 10^3~\text{J/m}^3 \)
2. \(2 \times 10^2 ~\text{J/m}^3 \)
3. \(1.8 \times 10^5 ~\text{J/m}^3 \)
4. \(2 \times 10^{-4} ~\text{J/m}^3 \)
1. \(1.8 \times 10^3~\text{J/m}^3 \)
2. \(2 \times 10^2 ~\text{J/m}^3 \)
3. \(1.8 \times 10^5 ~\text{J/m}^3 \)
4. \(2 \times 10^{-4} ~\text{J/m}^3 \)
Subtopic: Energy stored in Capacitor |
65%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Two capacitors \(C_1\) and \(C_2\) are connected in parallel to a battery. The 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?
1. \(C_2>C_1, U_2<U_1 \)
2. \( C_1> C_2, U_1< U_2 \)
3. \( C_1> C_2, U_1> U_2 \)
4. \({C}_2>{C}_1, {U}_2>{U}_1 \)
1. \(C_2>C_1, U_2<U_1 \)
2. \( C_1> C_2, U_1< U_2 \)
3. \( C_1> C_2, U_1> U_2 \)
4. \({C}_2>{C}_1, {U}_2>{U}_1 \)
Subtopic: Energy stored in Capacitor |
64%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Consider a parallel plate capacitor of are \(A\) (of each plate) and separation \(d\) between the plates. If \(E\) is the electric field and \(\varepsilon_0\) is the permittivity of free space between the plates, then the potential energy stored in the capacitor is:
1. \(\dfrac{1}{2} \varepsilon_0 {E}^2 {Ad}\)
2. \(\varepsilon_0 E^2 A d \)
3. \(\dfrac{1}{4} \varepsilon_0 {E}^2 {Ad}\)
4. \(\dfrac{3}{4} \varepsilon_0 {E}^2{Ad}\)
1. \(\dfrac{1}{2} \varepsilon_0 {E}^2 {Ad}\)
2. \(\varepsilon_0 E^2 A d \)
3. \(\dfrac{1}{4} \varepsilon_0 {E}^2 {Ad}\)
4. \(\dfrac{3}{4} \varepsilon_0 {E}^2{Ad}\)
Subtopic: Energy stored in Capacitor |
95%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A parallel-plate capacitor of capacitance \(40 \mu F\) is connected to a \(100 V\) power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant \(K=2\). Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are
1. \(4~\text{mC}~\text{and}~0.2~\text J\)
2. \(2~\text{mC}~\text{and}~0.4~\text J\)
3. \(8~\text{mC}~\text{and}~2.0~\text J\)
4. \(2~\text{mC}~\text{and}~0.2~\text J\)
1. \(4~\text{mC}~\text{and}~0.2~\text J\)
2. \(2~\text{mC}~\text{and}~0.4~\text J\)
3. \(8~\text{mC}~\text{and}~2.0~\text J\)
4. \(2~\text{mC}~\text{and}~0.2~\text J\)
Subtopic: Energy stored in Capacitor |
80%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A parallel plate capacitor of capacitance \(12.5~\text{pF}\) is charged by a battery connected between its plates to a potential difference of \(12.0~\text V.\) The battery is now disconnected, and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right) \) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is:
1. \(750\times 10^{-12}~\text J\)
2. \(900\times 10^{-12}~\text J\)
3. \(-750\times 10^{-12}~\text J\)
4. \(-900\times 10^{-12}~\text J\)
1. \(750\times 10^{-12}~\text J\)
2. \(900\times 10^{-12}~\text J\)
3. \(-750\times 10^{-12}~\text J\)
4. \(-900\times 10^{-12}~\text J\)
Subtopic: Energy stored in Capacitor |
61%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
The energy stored in the circuit \(1\) is \(E.\) If capacitors in the circuit \(1\) and the circuit \(2\) are connected in parallel as shown, the energy stored becomes \(\dfrac{x E}{6},\) then the value of \(x\) is:
1. \(50\)
2. \(40\)
3. \(30\)
4. \(20\)
1. \(50\)
2. \(40\)
3. \(30\)
4. \(20\)
Subtopic: Energy stored in Capacitor |
71%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A square loop of resistance \(16~\Omega\) is connected with a battery of \(9~\text{V}\) and an internal resistance of \(1~\Omega.\) In steady state, find the energy stored in a capacitor of capacity \({C}=4~\mu\text F\) as shown. (at steady state current divides symmetrically)
1. \(51.84~\mu\text{J}\)
2. \(12.96~\mu\text{J}\)
3. \(25.92~\mu\text{J}\)
4. \(103.68~\mu\text{J}\)
1. \(51.84~\mu\text{J}\)
2. \(12.96~\mu\text{J}\)
3. \(25.92~\mu\text{J}\)
4. \(103.68~\mu\text{J}\)
Subtopic: Energy stored in Capacitor |
53%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
Two capacitors are charged as shown in the figure. When both the positive terminals and negative terminals of capacitors are connected, then the energy loss is:
1. \(\dfrac{1}{2}{CV}^2\)
2. \(\dfrac{3}{4}{CV}^2\)
3. \(\dfrac{1}{4}{CV}^2\)
4. \(2{CV}^2\)
1. \(\dfrac{1}{2}{CV}^2\)
2. \(\dfrac{3}{4}{CV}^2\)
3. \(\dfrac{1}{4}{CV}^2\)
4. \(2{CV}^2\)
Subtopic: Energy stored in Capacitor |
73%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
© 2026 GoodEd Technologies Pvt. Ltd.