Select Question Set:
Q. No.An uncharged capacitor \((C)\) is connected to a battery of emf \(E\). Once it is fully charged, it is connected to a second battery of emf \(2E\). The positive terminal of the capacitor and battery are connected and their negative terminals are similarly connected together. The energy dissipated as heat, when the second battery is connected is:
1.
\(\dfrac{3}{2}CE^2\)
2.
\(\dfrac{1}{2}CE^2\)
3.
\(CE^2\)
4.
\(\dfrac{5}{2}CE^2\)
Subtopic: Energy stored in Capacitor |
50%
Level 3: 35%-60%
Hints
Find the charge on the \(3~\mu\text{F}\) capacitor.
1. \(1.5~\mu\text{C}\)
2. \(3~\mu\text{C}\)
3. \(4.5~\mu\text{C}\)
4. \(9~\mu\text{C}\)
1. \(1.5~\mu\text{C}\)
2. \(3~\mu\text{C}\)
3. \(4.5~\mu\text{C}\)
4. \(9~\mu\text{C}\)
Subtopic: Combination of Capacitors |
52%
Level 3: 35%-60%
Hints
Consider a spherical conductor of radius \(r\), centred at the point \(O\). A point charge \(q(q>0)\) is placed outside the sphere, at a distance '\(d\)' from its centre \((O)\) \((d>r)\) and the sphere is earthed.
Given below are two statements:
Given below are two statements:
| Assertion (A): | The electric flux due to the external charge \(q\) and the induced charges on the sphere through the spherical surface \(S\) shown dotted in the diagram, is \(\left(-\dfrac{q}{\varepsilon_0}\right)\). |
| Reason (R): | Negative charges are induced on the surface of the conducting sphere due to the positive charge \(q\) in the vicinity, and the potential of the conducting sphere is zero. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Capacitance |
51%
Level 3: 35%-60%
Hints
A parallel plate capacitor \((C)\) is charged by connecting it to a battery (EMF \(E\)). A dielectric slab is inserted into the space between the plates.
Choose the correct answer from the options given below:
| (I) | The charge on the plates increases. |
| (II) | The energy stored in the capacitor increases. |
| (III) | Work is done by the battery as the slab is inserted. |
Choose the correct answer from the options given below:
| 1. | (I), and (II) are True. |
| 2. | (I) and (III) are True. |
| 3. | only (I) is True. |
| 4. | (I), (II), and (III) are True. |
Subtopic: Capacitance |
64%
Level 2: 60%+
Hints
A capacitor is constructed by taking metallic circular discs of radius \(r\) placed face-to-face with a separation of \(d.\) A dielectric slab is inserted into the space between the plates so that it fills the entire width, but only half the area between the plates. The dielectric constant is \(K.\) Then, the capacitance is:
| 1. | \(\dfrac{K\varepsilon_0\pi r^2}{d}\) | 2. | \(\dfrac{K\varepsilon_0\pi r^2}{2d}\) |
| 3. | \(\dfrac{K+1}{2}\dfrac{\varepsilon_0\pi r^2}{d}\) | 4. | None of the above |
Subtopic: Dielectrics in Capacitors |
60%
Level 2: 60%+
Hints
A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following remains unchanged?
Choose the correct option from given ones:
| (I) | The charge on the plates. |
| (II) | The potential difference between the plates. |
| (III) | The energy stored in the capacitor. |
Choose the correct option from given ones:
| 1. | (I) only | 2. | (I) and (II) |
| 3. | (I) and (III) | 4. | (I), (II) and (III) |
Subtopic: Dielectrics in Capacitors |
72%
Level 2: 60%+
Hints
Two identical capacitors, each of capacitance \(C\), are connected in series and are charged by means of an ideal battery of emf \(E\). They are disconnected and reconnected in parallel and connected to the same battery. During this reconnection, the positive terminals of the capacitors are connected to the positive terminal of the battery and their negative terminals are similarly connected together. Let, the work done by the battery during the first connection be \(W_1\), and during the second be \(W_2\). Then,
| 1. | \(W_1=W_2\) | 2. | \(2W_1 =W_2\) |
| 3. | \(W_1 = 2W_2\) | 4. | \(4W_1 = W_2\) |
Subtopic: Energy stored in Capacitor |
Level 4: Below 35%
Hints
A metallic sphere of radius \(R\) is given a charge \(Q.\) The energy stored in the sphere due to this charge is:
1. \(\dfrac{Q^2}{4\pi\varepsilon_0R}\)
2. \(\dfrac{2Q^2}{4\pi\varepsilon_0R}\)
3. \(\dfrac12 \left ( \dfrac{Q^2}{4\pi\varepsilon_0R} \right )\)
4. \(\dfrac{Q^2}{16\pi\varepsilon_0R}\)
1. \(\dfrac{Q^2}{4\pi\varepsilon_0R}\)
2. \(\dfrac{2Q^2}{4\pi\varepsilon_0R}\)
3. \(\dfrac12 \left ( \dfrac{Q^2}{4\pi\varepsilon_0R} \right )\)
4. \(\dfrac{Q^2}{16\pi\varepsilon_0R}\)
Subtopic: Energy stored in Capacitor |
69%
Level 2: 60%+
Hints
In a certain region of space, equipotential surfaces of the electric field are drawn - corresponding to \(V=10\) volt and \(V=9.9\) volts. There is no field along the \(z\text-\)direction. At a certain point \(P,\) on the \(10-\)volt surface, the distance \(PQ_1,\) to the \(9.9\) volt surface is \(2\) mm when \(\overrightarrow{P Q}_{1}\) is along the \(x\text-\)axis. On the other hand, if \(\overrightarrow{P Q}_{2}\) is taken parallel to the \(y\text-\)axis, the corresponding distance \(PQ_2=1\) mm. The electric field at \(P\) is along:
| 1. | \(2 \hat{i}+\hat{j}\) | 2. | \(2 \hat{j}+\hat{i}\) |
| 3. | \(\dfrac{1}{4} \hat{i}+\hat{j}\) | 4. | \( \dfrac{1}{4} \hat{j}+\hat{i}\) |
Subtopic: Relation between Field & Potential |
53%
Level 3: 35%-60%
Hints
The capacitance of a parallel plate capacitor depends on the 'overlapping' or 'facing' area between the plates if the plates are very close together. A parallel plate capacitor is made by taking two metallic plates of the shape of equilateral triangles and placing them very close to each other at a uniform separation- facing each other. Their capacitance is now \(C_1.\) The two plates are now rotated in their planes about an axis perpendicular to their planes- passing through their centers - until their 'overlap' is least.
The capacitance is now \(C_2.\)
\(\dfrac{C_1} { C_2}\) equals:
The capacitance is now \(C_2.\)
\(\dfrac{C_1} { C_2}\) equals:
| 1. | \(3\) | 2. | \(2\) |
| 3. | \(\dfrac{3}{2}\) | 4. | \(\dfrac{4}{3}\) |
Subtopic: Capacitance |
55%
Level 3: 35%-60%
Hints
Select Question Set:
© 2025 GoodEd Technologies Pvt. Ltd.