Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 56

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Weekly Quiz Competition

Question 1
1 / -0

The equivalent capacitance between the point s $$A$$ and $$B$$ in the given diagram is

A
$$8\ \mu F$$

B
$$6\ \mu F$$

C
$$\dfrac {8}{3}\ \mu F$$

D
$$\dfrac {3}{8}\ \mu F$$

Solution
Question 2
1 / -0

For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that:-
$$V = \dfrac{q}{4 \pi \varepsilon_0 R_0}$$ for $$r \ R_0$$ and $$V = \dfrac{q}{4 \pi \varepsilon_0 r}$$ for $$ r \geq R_0$$.
Then which option is incorrect:

A
Total charge within $$2 R_0$$ is $$q$$.

B
Total electrostatic energy for $$ r \leq R_0$$ is zero

C
At $$r = R_0$$ electric field is discontinuous.

D
There will be no charge anywhere except at $$r = R_0$$

Solution

$$\begin{array}{l} V=\dfrac { q }{ { 4\pi { \varepsilon _{ o } }{ R_{ o } } } } \\ \therefore che\, \, is\, \, q \\ So\, \, option\, \, A\, \, is\, \, correct\, \\ E=0\, \, \, inside\, \, r={ R_{ o } } \\ =\frac { { Kq } }{ { { R^{ 2 } } } } \, \, \, \, \, outside\, \, r\ge { R_{ o } } \\ \therefore E\, \, is\, \, discontinuous\, \, of\, \, r={ R_{ o } } \\ So\, \, option\, \, C\, \, is\, \, correct \\ also\, \, there\, \, will\, \, be\, \, no\, \, che\, \, except\, \, at\, \, r={ R_{ o } } \\ So\, \, option\, \, D\, \, is\, correct. \\ electrostatics\, \, energy\, \, for\, \, r<{ R_{ o } } \\ is\, \, zero\, \, but\, \, if\, \, is\, \, not\, \, zero\, \, for\, \, r={ R_{ o } } \\ So\, \, option\, \, B\, \, is\, \, wrong \\ Hence, \\ option\, \, A,C\, \, and\, D\, \, is\, \, correct\, \, answer. \end{array}$$
Question 3
1 / -0

in a certain region of free space a non-uniform electric field which depends on x-coordinates is given by $$\vec E = E_0 x \hat i$$. What is the total amount of electric potential energy contained within the cube of sides of length L as shown below?

A
$$\dfrac{1}{5} \varepsilon_0 E_0^2 L^5$$

B
$$\dfrac{1}{5} \varepsilon_0 E_0^2 L^6$$

C
$$\dfrac{1}{6} \varepsilon_0 E_0^2 L^6$$

D
$$\dfrac{1}{2} \varepsilon_0 E_0^2 L^5$$

Solution

$$\begin{array}{l} from\, the\, given\, figure \\ du=\frac { 1 }{ 2 } { \varepsilon _{ 0 } }\left( { { t^{ 2 } } } \right) .\left( { { 1^{ 2 } }dx } \right) \\ =\frac { 1 }{ 2 } { \varepsilon _{ o } }{ L^{ 2 } }E_{ 0 }^{ 2 }\int _{ 0 }^{ L }{ { x^{ 2 } }dx } \\ =\frac { 1 }{ 2 } { \varepsilon _{ 0 } }{ L^{ 2 } }E_{ 0 }^{ 2 }\left( { \frac { { { L^{ 3 } } } }{ 3 } } \right) \\ =\frac { 1 }{ 2 } { \varepsilon _{ 0 } }{ L^{ 5 } }E_{ 0 }^{ 2 }. \\ Hence,\, the\, option\, D\, is\, the\, \, correct\, answer. \end{array}$$
Question 4
1 / -0

In the given circuit shown in the figure, what will be the charge stored in the capacitor of capacity $$5 \mu F$$ ?

A
0

B
1

C
2

D
3

Solution

Three capacitors of $$2\mu F$$ are connect in parallel combination thus giving a combine capacity of $$6\mu F\quad $$,which are connected in series connection with another capacitor of $$4\mu F.$$ Now remaining two capacitor of values $$5\mu F\quad and\quad 3\mu F$$ are short circuited making the charge on both these capacitor 0.
Refer the given simplified diagram.
Question 5
1 / -0

In the given circuit, the effactive capacitance between $$A$$ and $$B$$ will be

A
$$0.5\ \mu F$$

B
$$1.5\ \mu F$$

C
$$2\ \mu F$$

D
$$2.5\ \mu F$$
Question 6
1 / -0

The equivalent capacitance of the combination shown in figure is:

A
$$C$$

B
$$2C$$

C
$$C/2$$

D
none of these

Solution
Question 7
1 / -0

Four charges $$1$$ mc, $$2$$ mc, $$3$$ mc, ...$$6$$ mc are placed on at corner of a square of side $$1$$m. The square lies in XY plane with its centre at origin

A
The electric potential at origin at origin

B
The electric potential is zero every where along X axis

C
The electric potential is not zero along Z- axis

D
The electric potential is zero along Z- axis for any orientation of square in XY plane.

Solution

Electric field at origin= sum of electric field due to individual charges
Then,
option $$C$$ is correct because electric field is not zero along z-axis as a every point the potential equals sum of potential due to individual charges which can never be zero.
Question 8
1 / -0

In the adjacent figure, find the capacitance between points $$A$$ and $$B$$ if area of each plate is $$A$$ and separation between the plates is $$d$$.

A
$$ \dfrac { { \varepsilon }_{ 0 }A }{ d }$$

B
$$ 2\dfrac { { \varepsilon }_{ 0 }A }{ d }$$

C
$$ 3\dfrac { { \varepsilon }_{ 0 }A }{ d }$$

D
$$ \dfrac { { \varepsilon }_{ 0 }A }{ 2d }$$
Question 9
1 / -0

The charge after flow through circuit is after switch is closed

A
ZERO

B
10C

C
5C

D
30C
Question 10
1 / -0

A $$3\mu F$$ capacitor up to $$300\ volt$$ and $$2\mu F$$ is charged up to $$200\ volt$$. The capacitor are connected so that the plates of same polarity are connected together. The final potential difference between the plates of the capacitor after they are connected is :

A
$$220\ V$$

B
$$600\ V$$

C
$$280\ V$$

D
$$260\ V$$