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Q. No.A \(12 ~\mu \text{F}\) capacitor is charged by means of a \(6~\text{V}\) battery and the charged capacitor and the battery are connected in series so that their combined potential difference is twice as much. When a second unknown capacitor (initially uncharged) is connected across this combination, the first capacitor is observed to lose half of its initial charge.
The capacitance of the unknown capacitor is:
1. \(4 ~\mu \text{F}\)
2. \(6~ \mu \text{F}\)
3. \(24 ~\mu \text{F}\)
4. \(36 ~\mu \text{F}\)
Subtopic: Capacitance |
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An arrangement consisting of two concentric spherical shells A and B has a capacitance \(C_0\) between them. If the upper 'hemispherical' space between them is filled by a dielectric of relative permittivity \(K_1\) and the lower by one of relative permittivity \(K_2,\) the new capacitance will be:
| 1. | \(\left(K_{1}+K_{2}\right) C_{0}\) | 2. | \( \dfrac{K_{1}+K_{2}}{2} C_{0}\) |
| 3. | \(\dfrac{1}{2}\left(\dfrac{1}{K_{1}}+\dfrac{1}{K_{2}}\right) C_{0}\) | 4. | \( \dfrac{2 K_{1} K_{2}}{K_{1}+K_{2}} C_{0}\) |
Subtopic: Dielectrics in Capacitors |
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A uniform electric field exists in a certain region of space. The potential at the following points are given (all units are in SI):
• \(A \left ( 1, 0, 0 \right )\) \(V_{A}=2\) volt
• \(B \left ( 0, 2, 0 \right )\) \(V_{B}=4\) volt
• \(C \left ( 0, 0, 2 \right )\) \(V_{C}=6\) volt
• \(D \left ( 1, 1, 0 \right )\) \(V_{D}=-1\) volt
The component of the electric field along the \(x\text-\)axis is:
1. \(2\) V/m
2. \(8\) V/m
3. \(3\) V/m
4. \(-6\) V/m
• \(A \left ( 1, 0, 0 \right )\) \(V_{A}=2\) volt
• \(B \left ( 0, 2, 0 \right )\) \(V_{B}=4\) volt
• \(C \left ( 0, 0, 2 \right )\) \(V_{C}=6\) volt
• \(D \left ( 1, 1, 0 \right )\) \(V_{D}=-1\) volt
The component of the electric field along the \(x\text-\)axis is:
1. \(2\) V/m
2. \(8\) V/m
3. \(3\) V/m
4. \(-6\) V/m
Subtopic: Relation between Field & Potential |
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A parallel plate air capacitor having a plate separation \(d\) is charged, and the energy stored is \(U\). The force between the plates is:
| 1. | \(\dfrac Ud\) | 2. | \(\dfrac {2U}d\) |
| 3. | \(\dfrac U{2d}\) | 4. | \(\dfrac {\sqrt2U}d\) |
Subtopic: Energy stored in Capacitor |
60%
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Four uncharged capacitors and resistances are connected as shown and a potential difference is applied between \(P\) and \(Q\).
It is observed that \(V_A=V_B\) after a sufficiently long time.
Then:
It is observed that \(V_A=V_B\) after a sufficiently long time.
Then:
| 1. | \(\dfrac{C_1}{C_2}=\dfrac{C_3}{C_4}\) | 2. | \(\dfrac{C_1}{C_2}=\dfrac{R_3~C_3}{R_4~C_4}\) |
| 3. | \(\dfrac{C_1}{C_2}=\dfrac{R_4}{R_3}\) | 4. | \(\dfrac{C_1}{C_2}=\dfrac{R_4~C_3}{R_3~C_4}\) |
Subtopic: Capacitance |
From NCERT
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The arrangement shown in the figure is set up with capacitors initially uncharged, and the circuit is completed. A potential difference is imposed across \(AB\) so that the charge on the upper capacitor is doubled without changing its sign.
Then, \(V_{A}-V_{B}=\)
1. \(E_0\)
2. \(2E_0\)
3. \(-E_0\)
4. zero
Then, \(V_{A}-V_{B}=\)
1. \(E_0\)
2. \(2E_0\)
3. \(-E_0\)
4. zero
Subtopic: Capacitance |
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Three metallic spheres of radii \(r_1,~ r_2,~ r_3\) are connected by very long conducting wires to form an equilateral triangle. The capacitance of the system is:
1. \(4 \pi \varepsilon_{0}\left(r_{1}+r_{2}+r_{3}\right)\)
2. \(4 \pi \varepsilon_{0} \dfrac{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}{r_{1}+r_{2}+r_{3}}\)
3. \(4 \pi \varepsilon_{0}\left(\dfrac{1}{r_{1}}+\dfrac{1}{r_{2}}+\dfrac{1}{r_{3}}\right)^{-1}\)
4. \(4 \pi \varepsilon_{0} \sqrt{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}\)
1. \(4 \pi \varepsilon_{0}\left(r_{1}+r_{2}+r_{3}\right)\)
2. \(4 \pi \varepsilon_{0} \dfrac{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}{r_{1}+r_{2}+r_{3}}\)
3. \(4 \pi \varepsilon_{0}\left(\dfrac{1}{r_{1}}+\dfrac{1}{r_{2}}+\dfrac{1}{r_{3}}\right)^{-1}\)
4. \(4 \pi \varepsilon_{0} \sqrt{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}\)
Subtopic: Capacitance |
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Four identical point charges (\(q\) each) are placed at the four corners of a square of diagonal \(d.\) The potential at a point which is at a distance \(\dfrac{d}{2}\) above the centre of the square is:
\(\Big(k=\dfrac{1}{4\pi\varepsilon_0}\Big)\)
\(\Big(k=\dfrac{1}{4\pi\varepsilon_0}\Big)\)
| 1. | \(\dfrac{8~kq}{d}\) | 2. | \(\dfrac{4~kq}{d}\) |
| 3. | \(\dfrac{4\sqrt2~kq}{d}\) | 4. | \(\dfrac{\sqrt2~kq}{d}\) |
Subtopic: Electric Potential |
69%
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The capacitance of the system of three parallel plates of plate area \(A,\) plate separation \(d\) is measured between the center plate \((X)\) and the two outer plates \((Y)\) connected together. It is equal to:
1. \(\dfrac{2\varepsilon_0A}{d}\)
2. \(\dfrac{\varepsilon_0A}{2d}\)
3. \(\dfrac{\varepsilon_0A}{d}\)
4. \(\dfrac{4\varepsilon_0A}{d}\)
1. \(\dfrac{2\varepsilon_0A}{d}\)
2. \(\dfrac{\varepsilon_0A}{2d}\)
3. \(\dfrac{\varepsilon_0A}{d}\)
4. \(\dfrac{4\varepsilon_0A}{d}\)
Subtopic: Capacitance |
68%
From NCERT
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A non-conducting circular plate is uniformly charged and the potential at its center is \(V_0.\) If all the charge is collected and kept at its edge, then the potential will be:
| 1. | \(2V_0\) | 2. | \(\dfrac{V_0}{2}\) |
| 3. | \(\dfrac{V_0}{3}\) | 4. | \(\dfrac{V_0}{\sqrt2}\) |
Subtopic: Electric Potential |
53%
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