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Q. No.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:
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 |
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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 |
From NCERT
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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%
From NCERT
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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%
From NCERT
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The left plate \(A\) of an air capacitor is connected to the positive terminal while the right plate \(B\) is connected to the negative terminal of a cell of voltage \(V_0.\) Assume that the plate area is \(A,\) and the plate separation is \(d.\) If a slab of dielectric constant \(K\) is inserted into the space between the plates, the electric field in the dielectric will be: (compared to the air capacitor)
| 1. | more. |
| 2. | less. |
| 3. | equal. |
| 4. | more or less or equal depending on the value of \(K\). |
Subtopic: Dielectrics in Capacitors |
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The equivalent capacitance of the circuit between the points \(A~\text{and}~B\) is equal to:
1. \(2C\)
2. \(\dfrac{3C}{2}\)
3. \(3C\)
4. \(\dfrac{5C}{2}\)
1. \(2C\)
2. \(\dfrac{3C}{2}\)
3. \(3C\)
4. \(\dfrac{5C}{2}\)
Subtopic: Combination of Capacitors |
66%
From NCERT
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A particle \((P)\) of mass \(m\) is placed on the axis of a uniform circular ring of radius \(R\) and mass \(M.\) Its distance \((OP)\) from the centre \((O)\) of the ring is equal to \(R.\) Let the net gravitational field at the centre of the ring be \(g.\) Then, the gravitational potential energy of the interaction of the system is:
1. \(-MgR\)
2. \(-mgR\)
3. \(\dfrac{-MgR}{\sqrt2}\)
4. \(\dfrac{-mgR}{\sqrt2}\)
1. \(-MgR\)
2. \(-mgR\)
3. \(\dfrac{-MgR}{\sqrt2}\)
4. \(\dfrac{-mgR}{\sqrt2}\)
Subtopic: Electric Potential Energy |
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A uniformly charged metallic sphere holds a total charge \(Q_0\) and has a potential \(V_0.\) The total potential energy stored is:
| 1. | \(Q_0V_0\) | 2. | \(\dfrac{Q_0V_0}{2}\) |
| 3. | \(\dfrac{Q_0V_0}{4}\) | 4. | \(-Q_0V_0\) |
Subtopic: Electric Potential Energy |
62%
From NCERT
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