Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 26

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Question 1
1 / -0

One Volt is equal to:

A
1 Joule

B
1 Newton/Coulomb

C
1 Joule/Coulomb

D
1 Coulomb/Newton

Solution

The volt is a measure of electric potential. One volt is defined as the difference in electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points. It is also equal to the potential difference between two parallel, infinite planes spaced 1 meter apart that create an electric field of 1 newton per coulomb. Additionally, it is the potential difference between two points that will impart one joule of energy per coulomb of charge that passes through it. It can be expressed in terms of SI base units (m, kg, s, and A)
$$1 volt = \dfrac{1 Joule}{Coulomb}$$
Question 2
1 / -0

What is the S.I. unit of electric potential?

A
ampere

B
volt

C
volt.m

D
coulomb

Solution

An electric potential (also called the electric field potential or the electrostatic potential) is the amount of electric potential energy that a unitary point electric charge would have if located at any point of space, and is equal to the work done by an electric field in carrying a unit positive charge from infinity to that point.
This value can be calculated in either a static (time-invariant) or a dynamic (varying with time) electric field at a specific time in units of joules per coulomb, or volts (V). The electric potential at infinity is assumed to be zero.
Question 3
1 / -0

Identify the correct statement from below:

A
A will be at higher potential

B
B will be at higher potential

C
Both will be at same potential

D
Can't be said

Solution

Point A have positive charge.
More is the positive charge, more will be the potential. So, A will be at higher potential.
Question 4
1 / -0

The electric volt is a measure of electrical potential. Identify which of the following can be defined as a volt.

A
Opposition to electrical motion

B
Number of particles in motion

C
Work per unit charge

D
Field strength per unit of force

E
Electrostatic discharge

Solution

eV is defined as the kinetic energy gained by a unit charge $$e$$ when it is accelerated by a potential difference of 1 volt. As we know kinetic energy is the measure of work done, therefore, volt can be defined as work done per unit charge.
Question 5
1 / -0

Two charges $$+q$$ and $$-q$$ are kept apart. Then at any point on the right bisector of line joining the two charges

A
The electric field strength is zero

B
The electric potential is zero

C
Both electric potential and electric field strength are zero

D
Both electric potential and electric field strength are non-zero

Solution

At equatorial point
$${ E }_{ e }=\dfrac { 1 }{ 4\pi { \varepsilon }_{ 0 } } \dfrac { p }{ { r }^{ 3 } } $$
(directed from $$+q$$ to $$-q$$) and $${ V }_{ e }=0$$
Question 6
1 / -0

Four capacitors of equal capacitance have an equivalent capacitance $${ C }_{ 1 }$$ when connected in series and an equivalent capacitance $${ C }_{ 2 }$$ when connected in parallel. The ratio $$\dfrac { { C }_{ 1 } }{ { C }_{ 2 } } $$ is

A
$${ 1 }/{ 4 }$$

B
$${ 1 }/{ 16 }$$

C
$${ 1 }/{ 8 }$$

D
$${ 1 }/{ 12 }$$

Solution

Let capacitance of each capacitor is $$C$$.
In series, equivalent capacitance
$${ C }_{ 1 }=\dfrac { C }{ 4 } $$
In parallel, equivalent capacitance
$${ C }_{ 2 }=4C$$
$$\therefore \dfrac { { C }_{ 1 } }{ { C }_{ 2 } } =\dfrac { 1 }{ 16 } $$
Question 7
1 / -0

The intensity of electric field E due to charge Q at distance r.

A
$$E\propto r$$

B
$$E\propto \displaystyle\frac{1}{r^2}$$

C
$$E\propto \displaystyle\frac{1}{r}$$

D
$$E\propto \displaystyle\frac{1}{r^3}$$

Solution

According to Coulomb's Law:
$$E = k \frac{Q}{r^2}$$
where E is electric field, q is charge at a distance r and k is a constant. Therefore,
$$E \propto \frac{1}{r^2}$$
Question 8
1 / -0

Identify the dimension of electric potential,

A
$$L^{2}MT^{-3}I^{-1}$$

B
$$L^{1}MT^{-2}I^{-1}$$

C
$$L^{-2}MT^{-2}I^{-1}$$

D
none of the above

Solution

Work done $$=$$ charge $$\times $$ potential difference
or Force $$\times$$ distance $$=$$ (current\times time)$$\times $$ potential difference
or $$[MLT^{-2}]\times [L]=([IT])[V]$$
or $$[V]=[ML^2T^{-3}I^{-1}]$$
Question 9
1 / -0

Two charges are separated by a distance d. If the distance between them is doubled, how does the electric potential between them change?

A
It is doubled

B
It is halved

C
It is quartered

D
It is quadrupled

E
It is unchanged

Solution

Initial electric potential between the charges $$V= \dfrac{kq}{d}$$
New distance between the charges $$d' = 2d$$

Thus new electric potential $$V' = \dfrac{kq}{2d} =\dfrac{V}{2}$$
Question 10
1 / -0

What is the equivalent capacitance between $$A$$ and $$B$$ in the diagram below?

A
$$10F$$

B
$$5F$$

C
$$2.5F$$

D
$$0F$$

Solution

The equivalent capacitance of the two capacitors connected in parallel=$$3\mu F+2\mu F=5\mu F$$
This combination is in series with $$5\mu F$$ capacitor.
Hence final equivalent capacitance=$$\dfrac{5\times 5}{5+5}F=2.5F$$

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Electrostatic Potential and Capacitance Test - 26

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Electrostatic Potential and Capacitance Test - 26

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Question 1

1 Joule

1 Newton/Coulomb

1 Joule/Coulomb

1 Coulomb/Newton

Solution

Question 2

ampere

volt

volt.m

coulomb

Solution

Question 3

A will be at higher potential

B will be at higher potential

Both will be at same potential

Can't be said

Solution

Question 4

Opposition to electrical motion

Number of particles in motion

Work per unit charge

Field strength per unit of force

Electrostatic discharge

Solution

Question 5

The electric field strength is zero

The electric potential is zero

Both electric potential and electric field strength are zero

Both electric potential and electric field strength are non-zero

Solution

Question 6

$${ 1 }/{ 4 }$$

$${ 1 }/{ 16 }$$

$${ 1 }/{ 8 }$$

$${ 1 }/{ 12 }$$

Solution

Question 7

$$E\propto r$$

$$E\propto \displaystyle\frac{1}{r^2}$$

$$E\propto \displaystyle\frac{1}{r}$$

$$E\propto \displaystyle\frac{1}{r^3}$$

Solution

Question 8

$$L^{2}MT^{-3}I^{-1}$$

$$L^{1}MT^{-2}I^{-1}$$

$$L^{-2}MT^{-2}I^{-1}$$

none of the above

Solution

Question 9

It is doubled

It is halved

It is quartered

It is quadrupled

It is unchanged

Solution

Question 10

$$10F$$

$$5F$$

$$2.5F$$

$$0F$$

Solution

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