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 |

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Q19:

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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Q20:

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

Subtopic: Capacitance |

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Q21:

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.

$4 \pi \varepsilon_{0} \sqrt{r_{1}^{2}+r_{2}^{2}+r_{3}^{2}}$

Subtopic: Capacitance |

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Q22:

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:

$\Big(k=\dfrac{1}{4\pi\varepsilon_0}\Big)$

1.	$\dfrac{8~kq}{d}$	2.	$\dfrac{4~kq}{d}$
3.	$\dfrac{4\sqrt2~kq}{d}$	4.	$\dfrac{\sqrt2~kq}{d}$

Subtopic: Electric Potential |

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Q23:

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.

$\dfrac{4\varepsilon_0A}{d}$

Subtopic: Capacitance |

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Q24:

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 |

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Q25:

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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Q26:

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.

$\dfrac{5C}{2}$

Subtopic: Combination of Capacitors |

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Q27:

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.

$\dfrac{-mgR}{\sqrt2}$

Subtopic: Electric Potential Energy |

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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. $\dfrac {\sqrt2U}d$

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1.	$\dfrac Ud$	2.	$\dfrac {2U}d$
3.	$\dfrac U{2d}$	4.	$\dfrac {\sqrt2U}d$

A parallel plate air capacitor having a plate separation dd is charged, and the energy stored is UU. The force between the plates is: 1. Ud\dfrac Ud 2. 2Ud\dfrac {2U}d 3. U2d\dfrac U{2d} 4. √2Ud\dfrac {\sqrt2U}d

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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. $\dfrac {\sqrt2U}d$