Electric Potential & Capacitance - NEET 2019 Live Session Quiz

Figures shows the variation of electric field intensity $E$ versus distance $x$ . What is the
potential difference between the points at $x = 2 m$ and at $x = 6 m$ from O $?$

1. $30 V$
2. $60 V$
3. $40 V$
4. $80 V$

As per this diagram a point charge $+ q$ is placed at the origin O. Work done in taking another point charge $- Q$ from the point $A {c o -$ ordinates $(0,$ a) $}$ to another point $B {$ co-ordinates $(a, 0)}$ along the straight path $A B$ is -

1. $(-qQ4πε0a21a2)√2a<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mfrac><mrow><mo>-</mo><mi>q</mi><mi>Q</mi></mrow><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mfrac><mn>1</mn><msup><mi>a</mi><mn>2</mn></msup></mfrac><mo>)</mo><msqrt><mn>2</mn></msqrt><mi>a</mi></math>$
2. zero
3. $(qQ4πε0a21a2)1√2<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mfrac><mrow><mi>q</mi><mi>Q</mi></mrow><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mfrac><mn>1</mn><msup><mi>a</mi><mn>2</mn></msup></mfrac><mo>)</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac></math>$
4. $qQ4πε0a21a2)√2a<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>q</mi><mi>Q</mi></mrow><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><msup><mi>a</mi><mn>2</mn></msup></mrow></mfrac><mfrac><mn>1</mn><msup><mi>a</mi><mn>2</mn></msup></mfrac><mo>)</mo><msqrt><mn>2</mn></msqrt><mi>a</mi></math>$

Three concentric spherical shells have radii a, b and $c (a < b < c)$ and have surface charge densities $σ, - σ$ and $σ$ respectively. If $V_{A}$ $, V B <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>B</mi></msub></math> $ and $V C <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>C</mi></msub></math> $ denote the potentials of the three shells, then, for $c = a + b,$ we have-
1. $V C <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>C</mi></msub></math> = V B <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>B</mi></msub></math> = V A <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>A</mi></msub></math>$
2. $V C <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>C</mi></msub></math>$ $ = V A <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>A</mi></msub></math> \neq <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>\neq</mo></math> V B <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>B</mi></msub></math> $
3. $V C <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>C</mi></msub></math>$ $ = V B <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>B</mi></msub></math> \neq <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>\neq</mo></math> V A <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>A</mi></msub></math> $
4. $V C <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>C</mi></msub></math>$ $ \neq <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>\neq</mo></math> V B <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>B</mi></msub></math> \neq <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>\neq</mo></math> V A <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>A</mi></msub></math> $

Four electric charges $+ q, + q, - q$ and $- q$ are placed at the comers of a side 2L . (see figure). The electric potential at point A, midway between the two charges $+ q$ and + $q,$ is

1. Zero
2. $\frac{1}{4 π ε_{0}} \frac{2 q}{L} (1 + \sqrt{5})$
3. $14πε02qL(1+1√5)<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mrow><mn>2</mn><mi>q</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>5</mn></msqrt></mfrac></mrow></mfenced></math>$
4. $14πε02qL(1-1√5)<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac><mfrac><mrow><mn>2</mn><mi>q</mi></mrow><mi>L</mi></mfrac><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mn>1</mn><msqrt><mn>5</mn></msqrt></mfrac></mrow></mfenced></math>$

The charges, each $+ q,$ are placed at the corners of an isosceles triangle $A B C$ of sides $B C$ and $A C, 2 a . D$ and $E$ are the mid points of $B C$ and CA. the work done in taking charge $Q$ from $D$ to $E$ is -

1.   $3qQ4π∈0a<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>q</mi><mi>Q</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">π</mi><msub><mo>∈</mo><mn>0</mn></msub><mi mathvariant="normal">a</mi></mrow></mfrac></math>$
2.   $3qQ8π∈0a<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi>q</mi><mi>Q</mi></mrow><mrow><mn>8</mn><mi mathvariant="normal">π</mi><msub><mo>∈</mo><mn>0</mn></msub><mi mathvariant="normal">a</mi></mrow></mfrac></math>$
3.   $qQ4π∈0a<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>q</mi><mi>Q</mi></mrow><mrow><mn>4</mn><mi mathvariant="normal">π</mi><msub><mo>∈</mo><mn>0</mn></msub><mi mathvariant="normal">a</mi></mrow></mfrac></math>$
4. Zero

In a region the potential is represented by $V (x, y, z) = 6 x - 8 x y - 8 y + 6 y z,$ where $V$ is in
volts and $x, y, z$ are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is -
1. $6 \sqrt 5 <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math> N$
2. 30N
3. $24 N$
4. $4 \sqrt 35 <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>35</mn></msqrt></math> N$

Two identical charged spheres suspended from a common point by two massless strings of length l, are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as:
1. $v \propto x$
2. $v \propto x^{- \frac{1}{2}}$
3. $v \propto x^{- 1}$
4. $v \propto x^{\frac{1}{2}}$

Two identical thin rings, each of radius R meters, are coaxially placed at a distance R meters apart. If $Q_{1}$ coulomb and $Q_{2}$ coulomb uniformly spread on the two rings, the work done in moving a charge q from the center of one ring to that of other is-
`1. Zero
2. $\frac{q (Q_{1} - Q_{2}) (\sqrt{2} - 1)}{(\sqrt{2} . 4 {πε}_{0} R)}$
3. $\frac{q \sqrt{2} (Q_{1} + Q_{2})}{(4 {πε}_{0} R)}$
4. $\frac{q (Q_{1} + Q_{2}) (\sqrt{2} + 1)}{(\sqrt{2} . 4 {πε}_{0} R)}$

Three charges $Q, + q$ and $+ q$ are placed at the vertices of a right-angle isosceles triangle as shown in figure. The net electrostatic energy of configuration is zero. $Q$ is equal to-

1. $-q1+√2<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mi>q</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac></math>$
2. $\frac{- 2 q}{2 + \sqrt{2}}$
3. $- 2 q$
$4. + q$

10.

An elementary particle of mass m and charge e is projected with velocity v at a much more massive particle of charge Ze, where $Z > 0$ . What is the closest possible approach of the incident particle ?
1. $Ze22πε0mv2<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Z</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow></mfrac></math>$
2. $Ze4πε0mv2<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Z</mi><mi>e</mi></mrow><mrow><mn>4</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow></mfrac></math>$
3. $Ze28πε0mv2<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Z</mi><msup><mi>e</mi><mn>2</mn></msup></mrow><mrow><mn>8</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow></mfrac></math>$
4. $Ze8πε0mv2<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>Z</mi><mi>e</mi></mrow><mrow><mn>8</mn><mi>π</mi><msub><mi>ε</mi><mn>0</mn></msub><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow></mfrac></math>$

11.

64 small drops of mercury, each of radius 'r' and charge q are combined to form a big drop. The ratio of the surface density of the charge of each small drop to that of a big drop is-
1. 4:1
2. 1:4
3. 1:64
4. 64:1

12.

Five identical plates each of area $A$ are joined a shown in the figure. The distance between the plates is d. The plates are connected to a p.d. of V volts. The charge on plates 1 and 4 will be-

1. $ε0AVd,2ε0AVd<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac></math>$
2. $-ε0AVd,2ε0AVd<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac></math>$
3. $ε0AVd,-2ε0AVd<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac></math>$
4. $-ε0AVd,-2ε0AVd<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub><mi>A</mi><mi>V</mi></mrow><mi>d</mi></mfrac></math>$

13.

Calculate the reading of voltmeter between
$X$ and $Y$ then $(V X - V Y <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi>X</mi></msub><mo>-</mo><msub><mi>V</mi><mi>Y</mi></msub></math> )$ is equal to -

1. $10 V$
2. $13.33 V$
3. $3.33 V$
4. $10.33 V$

14.

Three capacitors of capacitors $C_{1}, C_{2}, C_{3}$ $$ are connected as shown in the figure. The points $A$ , $B$ and $C$ are at potential $_{1}$ and $_{3}$ respectively. Then the potential at $O$ will be $-$

1.   $\frac{V_{1} + V_{2} + V_{3}}{2}$ $ $
2.    $\frac{V_{1} V_{2} + V_{2} V_{3} + {V_{1}}_{2} V_{3}}{V_{1} + V_{2} + V_{3}}$ $ $
3.   $\frac{V_{1} C_{1} + V_{2} C_{2} + V_{3} C_{3}}{C_{1} + C_{2} + C_{3}}$
4. zero

15.

A circuit has a section $A B$ as shown in the fig. With $C_{1}$ and the potential difference $V_{A}$ . The voltage across $C_{1}$ $$ is-

1. zero
2. $5 V$
3. $10 V$
4. 15V

16.

A $1 μ F$ capacitor is connected in the circuit shown below. The e.m.f of the cell is 2 volts and the internal resistance is 0.5 ohm. The resistors $R_{1}$ $$ and $R_{2}$ have values of 4 ohms and 1 ohm respectively. The charge on the capacitor must be-

1. $2 μ C$
2. $1 μ C$
3. $1.33 μ C$
4. zero

17.

An infinite number of identical capacitors each of capacitance $1 μ F$ are connected as in
adjoining figure. Then the equivalent capacitance between $A$ and $B$ is-

1. $1 μ F$
2. $2 μ F$
3. $\frac{1}{2}$
4. $\infty$

18.

Two thin dielectric slabs of dielectric constants $K_{1}$ and $K_{2}$ are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field 'E' between the plates with distance 'd' as measured from plate $P$ is correctly shown by :

1.
2.
3.
4.

19.

A parallel plate air capacitor of capacitance C is connected to a cell of emf $V$ and then
disconnected from it. A dielectric slab of dielectric constant $K,$ which can just fill the air gap of the capacitor, is now inserted in it.
Which of the following is incorrect ?
1. The potential difference between the plates decreases K times
2. The energy stored in the capacitor decreases $K$ time.
3. The change in energy stored is $\frac{1}{2} C V^{2} (\frac{1}{K} - 1)$
4. The charge on the capacitor is not conserved.

20.

A parallel plate air capacitor has capacity ’ $C'$ , distance of separation between plates is ’ $d'$ and potential difference $' V'$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is :
1. $\frac{C^{2} V^{2}}{2 d^{2}}$
2. $\frac{C^{2} V^{2}}{2 d}$
3. $\frac{C V^{2}}{2 d}$
4. $\frac{C V^{2}}{d}$

21.

A capacitor of 2 $μ F$ is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:

1. 20%
2. 75%
3. 80%
4. 0%

22.

The effective capacitance between the points P and Q of the arrangement shown in the figure. is -

1. (1/2) $μ F$
2. 1 $μ F$
3. 2 $μ F$
4. 1.33 $μ F$

23.

When the key is pressed at time t = 0 then which of the following statement about the current i in the resistor AB of the given circuit is true -

1. at t = 0, i = 2mA and with time it goes to 1mA
2. i oscillates between 1 mA and 2 mA
3. i = 2 mA at all t
4. i = 1 mA at all t

24.

The combination of capacitors with $C_{1}$ $= 3 μ F,$ $C_{2}$ and $C_{3}$ is charged by connecting AB to a battery. Consider the following statements -
(I) Energy stored in $C_{1}$ $ =$ Energy stored in $C_{2}$ $ +$ Energy stored in $C_{3}$ $$
(II) Charge on $C_{1}$ $=$ Charge on $C_{2}$ $$ $+$ Charge on $C_{3}$ $$
(III) Potential drop across $C_{1}$ $ =$ Potential drop across $C_{2}$ $ =$ Potential drop across $C_{3}$ $$
Which of these are correct $-$

1. I and II
2. II only
3. I and III
4. III only

25.

In an LCR circuit as shown below both switches are open initially. Now switch $S_{1}$ $$ is closed $S_{2}$ kept open. $(q$ is charge on the capacitor and $τ$ $= R C$ is Capacitive time constant). Which of the following statement is correct $?$

1. $^{- 2}$
2. $\frac{τ}{2}$
3. Work done by the battery is half of the energy dissipated in the resistor
4. At t= $τ, q=CV/2$

26.

A parallel plate capacitor having plates of area S and plate separation d, has apacitance $C_{1}$ in air. When two diclectrics of different relative permittivities $ε_{1}$ and $ε_{2}$ are introduced between the two plates as shown in the figure, the capacitance becomes $C_{2}$ . The ratio $\frac{C_{2}}{C_{1}}$ is

1.   $6 / 5$
2.   $5 / 3$
3.   $7 / 5$
$4. 7 / 3$

27.

A combination of capacitors is set up as shown in the figure. The magnitude of the electric ficld, due to a point charge Q (having a charge equal to the sum of the charges on the $4 μ F$ and $9 μ F$ capacitors), at a point distant $30 m$ from it, would equal -

1. $240 N / C$
2. $360 N / C$
3. $420 N / C$
4. $480 N / C$

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