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Q. No.Five capacitors of capacitances;
\(C_1=C_2=C_3=C_4 = 10~\mu\text{F}\) and \(C_5 = 2.5~\mu\text{F}\) are connected as shown, along with a battery of \(50\) V.
The equivalent capacitance and the charges on each capacitor, respectively, are:
1. \(5~\mu\text{F}, 125~\mu\text{C}\) on all capacitors
2. \(5~\mu\text{F}, 250~\mu\text{C}\) on all capacitors
3. \(4~\mu\text{F}, 250~\mu\text{C}\) on \(C_1\) to \(C_4\) and \(125~\mu\text{C}\) on \(C_5\)
4. \(5~\mu\text{F}, 125~\mu\text{C}\) on \(C_1\) to \(C_4\) and \(25~\mu\text{C}\) on \(C_5\)
\(C_1=C_2=C_3=C_4 = 10~\mu\text{F}\) and \(C_5 = 2.5~\mu\text{F}\) are connected as shown, along with a battery of \(50\) V.
The equivalent capacitance and the charges on each capacitor, respectively, are:
1. \(5~\mu\text{F}, 125~\mu\text{C}\) on all capacitors
2. \(5~\mu\text{F}, 250~\mu\text{C}\) on all capacitors
3. \(4~\mu\text{F}, 250~\mu\text{C}\) on \(C_1\) to \(C_4\) and \(125~\mu\text{C}\) on \(C_5\)
4. \(5~\mu\text{F}, 125~\mu\text{C}\) on \(C_1\) to \(C_4\) and \(25~\mu\text{C}\) on \(C_5\)
Subtopic: Combination of Capacitors |
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Consider two uncharged capacitors of equal capacitance \(200~\text{pF}.\) One of them is charged by a \(100~\text{V}\) supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is:
1. \(1.0\times 10^{-6}~\text{J}\)
2. \(0.5\times 10^{-6}~\text{J}\)
3. \(0.5~\text{J}\)
4. \(1.0~\text{J}\)
1. \(1.0\times 10^{-6}~\text{J}\)
2. \(0.5\times 10^{-6}~\text{J}\)
3. \(0.5~\text{J}\)
4. \(1.0~\text{J}\)
Subtopic: Energy stored in Capacitor |
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Which of the following statements are correct?
Choose the correct answer from the options given below:
1. \(\mathrm{C,D~\text{and}~E}~\text{only}\)
2. \(\mathrm{A,B~\text{and}~D}~\text{only}\)
3. \(\mathrm{A,C~\text{and}~D}~\text{only}\)
4. \(\mathrm{A,C~\text{and}~E}~\text{only}\)
| \(\mathrm{A.}\) | Inside a conductor, the electrostatic field is zero. |
| \(\mathrm{B.}\) | The electric field at the surface of a charged conductor does not depend on its surface charge density. |
| \(\mathrm{C.}\) | The interior of a charged conductor can have no excess charge in the static situation. |
| \(\mathrm{D.}\) | At the surface of a charged conductor, the electrostatic field must be normal to the surface at every point. |
| \(\mathrm{E.}\) | The electrostatic potential is zero everywhere inside a charged conductor. |
1. \(\mathrm{C,D~\text{and}~E}~\text{only}\)
2. \(\mathrm{A,B~\text{and}~D}~\text{only}\)
3. \(\mathrm{A,C~\text{and}~D}~\text{only}\)
4. \(\mathrm{A,C~\text{and}~E}~\text{only}\)
Subtopic: Electrostatic Shielding |
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Three identical capacitors, \(P,\) \(Q\) and \(S,\) each of the capacitance \(C,\) are connected to a battery of voltage \(V,\) as shown in the figure. If the energy stored in the capacitor \(P\) and total energy stored in the system are \(U_P\) and \(U_T,\) respectively, then the ratio \(\dfrac {U_P}{U_T}\) is:
2.
3.
4.
Subtopic: Energy stored in Capacitor |
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A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius \(R,\) having uniform positive charge density \(\rho,\) as shown in the figure. The initial and final positions of the charge are marked by \(A\) and \(B\) at distances \(2R\) and \(3R\) respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is \( \dfrac{\rho R^2}{n \epsilon_0}.\) The value of \(n\) is: (\(\varepsilon _0\) is the permittivity of vacuum)
1. \(18\)
2. \(2\)
3. \(6\)
4. \(9\)
1. \(18\)
2. \(2\)
3. \(6\)
4. \(9\)
Subtopic: Electric Potential |
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Consider a fixed uniformly charged insulating sphere with radius \(R\) and total charge \(+Q.\) A point charge \(-q\left ( q\ll Q \right )\) with mass \(m\) is released from rest at a distance of \(3R\) from the centre of charged sphere. When the point charge reaches the surface of the sphere, its speed is:
(\(\epsilon_o\) is the permittivity of vacuum, neglecting gravitational forces)
(\(\epsilon_o\) is the permittivity of vacuum, neglecting gravitational forces)
| 1. | \(\sqrt{\dfrac{Qq}{4\pi\epsilon_0 mR}}~\) | 2. | \(\sqrt{\dfrac{3Qq}{4\pi\epsilon_0 mR}}~\) |
| 3. | \(\sqrt{\dfrac{2Qq}{3\pi\epsilon_0 mR}}~\) | 4. | \(\sqrt{\dfrac{Qq}{3\pi\epsilon_0 mR}}~\) |
Subtopic: Electric Potential Energy |
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A point charge \(Q\) is placed inside a cavity within a solid, isolated conducting sphere. Consider points \(A,B\) and \(C\) as shown in the figure, where the magnitudes of the electric fields are \(E_A\), \(E_B\) and \(E_C\), respectively. The points \(B\) and \(C\) are at the same distance from the centre of the solid sphere. The correct option is:
| 1. | \(E_A \neq 0, E_B < E_C\) | 2. | \(E_A = 0, E_B = E_C\) |
| 3. | \(E_A \neq 0, E_B = E_C\) | 4. | \(E_A = 0, E_B > E_C\) |
Subtopic: Electrostatic Shielding |
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An electric dipole with dipole moment \(5\times10^{-6}~\text{C-m} \) is aligned with the direction of a uniform electric field of magnitude \(4\times10^{5}~\text{N/C}. \) The dipole is then rotated through an angle of \(60^\circ\) with respect to the electric field. The change in the potential energy of the dipole is:
| 1. | \(1.2~\text{J}\) | 2. | \(1.5~\text{J}\) |
| 3. | \(0.8~\text{J}\) | 4. | \(1.0~\text{J}\) |
Subtopic: Energy of Dipole in an External Field |
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The plates of a parallel plate capacitor are separated by \(d.\) Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(\dfrac{3}{8} d\) and \(\dfrac{d}{2},\) respectively are inserted in the capacitor. Due to this, the capacitance become two times larger than when there is nothing between the plates.
If \(K_1=1.25 ~K_2,\) the value of \(K_1\) is:
1. \(1.60\)
2. \(1.33\)
3. \(2.66\)
4. \(2.33\)
If \(K_1=1.25 ~K_2,\) the value of \(K_1\) is:
1. \(1.60\)
2. \(1.33\)
3. \(2.66\)
4. \(2.33\)
Subtopic: Dielectrics in Capacitors |
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
In the light of the above statements, choose the correct answer from the options given below:
| Assertion (A): | The potential \((V)\) at any axial point, at \(2~\text m\) distance (\(r\)) from the centre of the dipole of dipole moment vector \(\vec P\) of magnitude, \(4\times10^{-6}~\text{C m},\) is \(\pm9\times10^3~\text{V}.\) (Take \({\dfrac{1}{4\pi\varepsilon_0}}=9\times10^9\) SI units) |
| Reason (R): | \(V=\pm{\dfrac{2P}{4\pi\varepsilon_0r^2}},\) where \(r\) is the distance of any axial point situated at \(2~\text m\) from the centre of the dipole. |
| 1. | Both (A) and (R) are True and (R) is not the correct explanation of (A). |
| 2. | (A) is True but (R) is False. |
| 3. | (A) is False but (R) is True. |
| 4. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
Subtopic: Electric Potential |
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