Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 25

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Question 1
1 / -0

Eight identical spherical mercury drops charged to a potential of 20 v each are coalesced into a single spherical drop:

A
The internal Energy of the system remains the same

B
The new potential of the drop is 80 V

C
Internal Energy of he system decreases

D
The potential remains the same i.e. 20 v

Solution

$$V=\dfrac {kq}{r}=20V$$
$$\dfrac {4}{3}\pi R^3=8\times \dfrac {4}{3}\pi r^3\Rightarrow R=2r$$
$$Q'=8q$$
$$V'=\dfrac {kQ'}{R}=\dfrac {k\times 8q}{2r}=\dfrac {4kq}{r}=4\times 20$$

$$V'=80 V$$
Question 2
1 / -0

To obtain $$3 \mu F$$ capacity from three capacitors of $$2 \mu F$$ each, they will be arranged as follows:

A
all the three in series

B
all the three in parallel

C
two capacitors in series and the third in parallel with the combination of first two

D
two capacitors in parallel and the third in series with the combination of first two

Solution

Adding all the capacitors in series creates a capacitance of $$2/3\mu F$$
Adding all the capacitors in parallel creates a capacitance of $$ 6\mu F$$
Adding two in series and third in parallel with both creates a capacitance of $$ 2/2 \mu F + 2 \mu F = 3 \mu F $$
Adding two in parallel and third in series creates a capacitance of $$ (4\times 2)/ (4+2) \mu F = 4/3 \mu F $$
Question 3
1 / -0

When a thin mica sheet is placed between the plates of a condenser then the amount of charge, so compared to its previous value, on its plates will become:

A
unchanged

B
zero

C
less

D
more

Solution

As no cell is connected to the capacitor, the charge will remain constant.
Question 4
1 / -0

Name the unit of electrical potential :

A
Coulomb

B
Watt

C
Joule

D
Volt

Solution

Answer is D.

The volt is a measure of electric potential. Electrical potential is a type of potential energy, and refers to the energy that could be released if electric current is allowed to flow.
Question 5
1 / -0

Electric potential is :

A
a scalar quantity

B
a vector quantity

C
neither scalar nor vector

D
sometimes scalar and sometimes vector

Solution

Electric potential is the electric potential energy per unit charge. In equation form, $$V=U/q,$$ where $$U$$ is the potential energy, $$q$$ is the charge, and $$V$$ is the electric potential. Since both the potential energy and charge are scalar quantities, so does the potential.
Question 6
1 / -0

Let S be the set of all points in a plane. Let R be a relation on S such that for any two points a and b, aRb iff b is within 1 cm from a. Then R is

A
Equivalence relation

B
Reflexive and symmetric not transitive

C
Reflexive and transitive not symmetric

D
Symmetric and transitive not reflexive

Solution

R is reflexive since any point is at distance O from itself so that it is within 1 cm from itselt.
R is symmetric since if a point a is within 1 cm from another point b, then b is also within 1 cm from a.
R is not transitive. Let a, b, c, be three points in a straight lines in this order such that distance between a and b is $$\frac{1}{2}$$ cm and distance between band c is $$\frac{2}{3}$$ cm. Then aRb and bRc. But (a, c) distance between a $$\not{\varepsilon}$$ R since the and c is $$\displaystyle \left ( \frac{1}{2} + \frac{2}{3} \right ) = \frac{7}{6} cm > 1 cm.$$
Question 7
1 / -0

1 volt = ?

A
1 joule

B
1 joule per coulomb

C
1 coulomb per metre

D
1 newton per coulomb

Solution

Using: $$V = \dfrac{W}{q}$$
$$\implies$$ 1 volt is equal to 1 joule per coulomb
Question 8
1 / -0

When a dielectric is introduced between the plates of a condenser, the capacity of condenser :

A
increases

B
decreases

C
remains same

D
none of these

Solution

If the empty Condensor has capacity $$C$$, then its capacity with dielectric is given by $$C' = kC$$, where $$k$$ is the dielectric constant of the dielectric material. $$k$$ can never be less than $$1$$.
Question 9
1 / -0

The equivalent capacitance in the given circuit is

A
$$3 \mu F$$

B
$$1.5 \mu F$$

C
$$2 \mu F$$

D
$$1 \mu F$$

Solution

Two 1.5 $$\mu$$ F capacitors are in parallel
$$\therefore C_p = 1.5 + 1.5 = 3 \mu F$$
Three $$3 \mu F$$ capacitors are in series
$$|therefore \displaystyle \frac{1}{C_{eq}} = \frac{1}{3} +\frac{1}{3} +\frac{1}{3} = \frac{3}{3} =1$$
$$\therefore c_{eq} = 1 \mu F$$
Question 10
1 / -0

what is the potential difference between two points, if 2J of work must be done to move a 4 mC charge from one point to another is:

A
50 V

B
500 V

C
5 V

D
5000 V

Solution

Answer is B.

The total work done = energy transferred.
so, we might see the equation energy = voltage x charge, E = V * Q, written as,
work = voltage x charge, W = V * Q.
In this case, the charge is 4 mC, that is, 0.004 C and work done is 2 J.
Therefore, V=W/Q = 2/0.004 = 500 V.
Hence, the potential difference between two points if 2 J of work must be done to move a 4 mC charge from one point to another is 500 V.

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Electrostatic Potential and Capacitance Test - 25

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Electrostatic Potential and Capacitance Test - 25

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Question 1

The internal Energy of the system remains the same

The new potential of the drop is 80 V

Internal Energy of he system decreases

The potential remains the same i.e. 20 v

Solution

Question 2

all the three in series

all the three in parallel

two capacitors in series and the third in parallel with the combination of first two

two capacitors in parallel and the third in series with the combination of first two

Solution

Question 3

unchanged

zero

less

more

Solution

Question 4

Coulomb

Watt

Joule

Volt

Solution

Question 5

a scalar quantity

a vector quantity

neither scalar nor vector

sometimes scalar and sometimes vector

Solution

Question 6

Equivalence relation

Reflexive and symmetric not transitive

Reflexive and transitive not symmetric

Symmetric and transitive not reflexive

Solution

Question 7

1 joule

1 joule per coulomb

1 coulomb per metre

1 newton per coulomb

Solution

Question 8

increases

decreases

remains same

none of these

Solution

Question 9

$$3 \mu F$$

$$1.5 \mu F$$

$$2 \mu F$$

$$1 \mu F$$

Solution

Question 10

50 V

500 V

5 V

5000 V

Solution

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