Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

A proton is accelerated through 70,000 V. Its energy will increase by

A
\(11200 eV\)

B
\(11200 \times 10^{15}J\)

C
\(5000 J\)

D
\(50,000 J\)

Solution

Kinetic energy K = Q.V ⇒ K = (+e) (70000V)

= 70000 eV = \(70000 \times 1.6 \times 10^{19}J\)

= \(11200 \times 10^{15}J\)
Question 2
1 / -0

The work done in bringing a 40 coulomb charge from point A to point B for distance 0.4 m is 5J. The potential difference between the two points will be (in volt)

A
0.2

B
124

C
0.125

D
0.40

Solution

By using W = \(Q. \triangle V\)

\(\triangle V = \frac{5}{40}\)

= 0.125 volt
Question 3
1 / -0

A parallel plate condenser has a capacitance of 60 µF in air and 200 µF when immersed in oil. The dielectric constant ′k′ of the oil is

A
3.45

B
33.3

C
1.10

D
3.33

Solution

\(C_{medium} = KC_{air}\)

\(K = \frac{C_{medium}}{C_{air}}\)

= \(\frac{200}{60}\)

= 3.33
Question 4
1 / -0

Assertion: If the distance between parallel plates of a capacitor is halved and dielectric constant is made three times, then the capacitor becomes 6 times.

Reason: Capacity of the capacitor does not depend upon the nature of the material.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(C) If assertion is true but reason is false.

(D) If the assertion and reason both are false.

(E) If assertion is false but reason is true

A
A

B
B

C
C

D
D

Solution

By the formula capacitance of a capacitor

\(C_1 = \varepsilon_0 \times \frac{KA}{d} \propto \frac{K}{d}\)

\(\frac{C_1}{C_2} = \frac{K_1}{d_1} \times \frac{d_2}{K_2}\)

= \(\frac{K_1}{K_2} \times \frac{\frac{d}{2}}{3K} = \frac{1}{6}\)

or \(C_2 = 6 C_1\)

C = \(\frac{Q}{V}\)

Again for capacity of a capacitor C = \(\frac{Q}{V}\). Therefore, capacity of a capacitor does not depend upon the nature of the material of the capacitor.
Question 5
1 / -0

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is

A
8 times

B
4 times

C
2 times

D
32 times

Solution

Volume of 8 small drops = Volume of big drop

\(8 \times \frac{4}{3} \pi r^3 = \frac{4}{3} \pi R^3\)

R = 2r, hence capacity becomes 2 times.
Question 6
1 / -0

The distance between the circular plates of a parallel plate condenser 40 mm in diameter, in order to have same capacity as a sphere of radius 1 metres

A
0.01 mm

B
0.1 mm

C
1.0 mm

D
10 mm

Solution

\(4 \pi \varepsilon_0 r = \frac{\varepsilon_0 A}{d}\)

d = \(\frac{A}{4 \pi r} = \frac{\pi (20 \times 10^{-3})^2}{4 \pi \times 1}\)

= 0.1 mm
Question 7
1 / -0

The capacitance of a metallic sphere will be 1µF, if its radius is nearly

A
9 km

B
10 m

C
1.11 m

D
1.11 cm

Solution

\(4 \pi \varepsilon_0 r = 1 \times 10^{-6}\)

r = \(10^{-6} \times 9 \times 10^9\)

= 9 km
Question 8
1 / -0

A parallel plate capacitor of a capacitance of 1 farad would have the plate area about

A
\(0.113 \; m^2\)

B
\(1 \;Km^2\)

C
\(100 \;Km^2\)

D
\(1000 \;Km^2 \)

Solution

Capacitance, C = 1 F

Let

d = 1 pm

= \(1 \times 10^{-12} m\)

Capacitance,

\(C = \frac{\varepsilon_0 A}{d} \)

\(A = \frac{Cd}{\varepsilon_0}\)

= \(\frac{1 \times 1 \times 10^{-12}}{8.854 \times 10^{-12}}\)

= \(= 0.113 m^2\)
Question 9
1 / -0

Energy stored in capacitor and dissipated during charging a capacitor bear a ratio

A
\(1:1\)

B
\(1:2\)

C
\(1:\frac{1}{2}\)

D
\(2:1\)

Solution

Half of the energy is dissipated during charging a capacitor.

Hence, \(\frac{energy\;stored\;in\;a\;capacitor}{energy\;dissipated\;during\;charging\;a\;capacitor}\)

= \(\frac{2}{1}\)

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Electrostatic Potential and Capacitance Test - 20

Result

Electrostatic Potential and Capacitance Test - 20

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SHARING IS CARING

Question 1

\(11200 eV\)

\(11200 \times 10^{15}J\)

\(5000 J\)

\(50,000 J\)

Solution

Question 2

0.2

124

0.125

0.40

Solution

Question 3

3.45

33.3

1.10

3.33

Solution

Question 4

A

B

C

D

Solution

Question 5

8 times

4 times

2 times

32 times

Solution

Question 6

0.01 mm

0.1 mm

1.0 mm

10 mm

Solution

Question 7

9 km

10 m

1.11 m

1.11 cm

Solution

Question 8

\(0.113 \; m^2\)

\(1 \;Km^2\)

\(100 \;Km^2\)

\(1000 \;Km^2 \)

Solution

Question 9

\(1:1\)

\(1:2\)

\(1:\frac{1}{2}\)

\(2:1\)

Solution

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