Electrostatics Test

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Electrostatics Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

Here is a combination of three identical capacitors. If resultant capacitance is 1 μƒ, calculate capacitance of each capacitor.

A
6 μƒ

B
3 μƒ

C
4 μƒ

D
2 μƒ

Solution

Combination of Capacitors in Series
C(effective) = C/3 = 1
Question 2
1 / -0

If the potential difference of a 6µF capacitor is changed from 10V to 20V, the increase in energy stored will be

A
2×10^–4 J

B
3×10^–4 J

C
4×10^–4 J

D
9×10^–4 J

Solution

Definition
Question 3
1 / -0

If two spheres of different radii have equal charge, then the potential will be

A
dependent on nature of material of the spheres.

B
more on smaller sphere

C
more on bigger sphere

D
equal on both spheres

Solution

When equal charges are given to two spheres of different radii, the potential will be more or the smaller sphere as per the equation, Potential = Charge / Radius.
Since potential is inversely proportional to radius, the smaller radius will have higher potential and vice versa.
Question 4
1 / -0

The capacitor preferred for high-frequency circuit is

A
Air capacitor

B
Mica capacitor

C
Electrolytic capacitor

D
None of the above

Solution

Mica capacitor. Mica capacitors have low resistive and inductive components associated with it. Hence, they have high Q factor and because of high Q factor their characteristics are mostly frequency independent, which allows this capacitor to work at high frequency.
Question 5
1 / -0

Three different capacitors are connected in series, then:

A
they will have equal charges

B
they will have same potential

C
both 1 & 2

D
none of these

Solution

C = Q/V
series connection splits the battery potential, hence....
V = V₁ + V₂
V₁ = Q/C₁ & V₂ = Q/C₂
Therefore, both have equal charge
Question 6
1 / -0

Calculate the equivalent capacitance for the following combination between points A and B

A
12/5 μƒ

B
5 μƒ

C
40/9 μƒ

D
37/5 μƒ

Solution

4μf and 6μf are in series (right side of AB) so 6x(4/6)+4=24/10μf
And now 5 μf and the resulting of above two are in parallel (as on different sides of AB) so 5+(24/10) =50+(24/10)=74/10=37/5μf
Question 7
1 / -0

There are three capacitors with equal capacitance. In series combination, they have a net capacitance of C₁and in parallel combination, a net capacitance of C₂.What will be the value of C₁ C₂?

A
1:9

B
3:2

C
2:3

D
9:1

Solution

For series combination,
1/C1=(1/C)+(1/C)+(1/C) [ Since all capacitors have equal capacitances]=3/C Or
C1=C/3−−−(i)
For parallel combination,
C2=C+C+C=3C−−−(ii)
Now,C1/C2=(C/3)/3C=(C/3)×(1/3C)=1/9
Question 8
1 / -0

Two capacitors of 20 μƒ and 30 μƒ are connected in series to a battery of 40V. Calculate charge on each capacitor.

A
480 μC

B
478 μC

C
450 μC

D
500 μC

Solution

C1= 20×10µf
and C2= 30×10µf
in series Ceq = C1C2/(C1+C2)
Ceq = 20×10^(-6)×30×10^(-6)/20×10^(-6)+30^×10(-6)
Ceq= 12×10^(-6)f
As we know that Q = CV
Putting the values of C and V= 40V, we get
Q = (12 * 10^-6) * 40
= 480µC
Question 9
1 / -0

Two capacitors of equal capacity are first connected in parallel and then in series. The ratio of the total capacities in the two cases will be

A
2 : 1

B
1 : 2

C
4 : 1

D
1 : 4

Solution

Third capacitor is short-circuited as its both ends are connected to B. Equivalent circuit is
Ceq=C+C=2C
Question 10
1 / -0

When two capacitors C₁ and C₂ are connected in series and parallel, their equivalent capacitances comes out to be 3μƒ and 16μƒ respectively. Calculate values of C₁ and C₂.

A
4μƒ and 12μƒ

B
6μƒ and 10μƒ

C
4μƒ and 10μƒ

D
6μƒ and 12μƒ

Solution

Let C_p be the equivalent capacitance of parallel
C_p=C₁+C₂
16= C₁+C₂……..(1)
Let Cs be the equivalent of capacitance in series
1/C_s=(1/C₁) + (1/C₂)
Or, C_s=C₁C₂/C₁+C₂
Or,3=C₁C₂/16
Or,C₂C₁=48
C₂=48/C₁……..(ii)
16=C1+48/C1
(C₁²-16C₁+48)=0
(C₁-4)(C₁-12)=0
C₁=4 ; C₁=12
If,
C₁=4
C₂=12
If,
C₂=4
C₁=12
So, the answer is, Either 12μf or4μf

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Electrostatics Test - 19

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Electrostatics Test - 19

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Question 1

6 μƒ

3 μƒ

4 μƒ

2 μƒ

Solution

Question 2

2×10–4 J

3×10–4 J

4×10–4 J

9×10–4 J

Solution

Question 3

dependent on nature of material of the spheres.

more on smaller sphere

more on bigger sphere

equal on both spheres

Solution

Question 4

Air capacitor

Mica capacitor

Electrolytic capacitor

None of the above

Solution

Question 5

they will have equal charges

they will have same potential

both 1 & 2

none of these

Solution

Question 6

12/5 μƒ

5 μƒ

40/9 μƒ

37/5 μƒ

Solution

Question 7

1:9

3:2

2:3

9:1

Solution

Question 8

480 μC

478 μC

450 μC

500 μC

Solution

Question 9

2 : 1

1 : 2

4 : 1

1 : 4

Solution

Question 10

4μƒ and 12μƒ

6μƒ and 10μƒ

4μƒ and 10μƒ

6μƒ and 12μƒ

Solution

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2×10^–4 J

3×10^–4 J

4×10^–4 J

9×10^–4 J