PG Brainstormer - 1C

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PG Brainstormer - 1C

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PG Brain Stormer - 1 CELECTROSTATICS, CAPACITANCE & CURRENT ELECTRICITY

An Ultimate Tool to understand advanced High School Physics by ASHISH ARORA Sir

Time Allowed 45 Min

Maximum Marks 55

Instruction : In Section A each question is of 3 Marks and there is a negative marking of -1 Mark whereas in Section Bthere is no negative marking and each question is of 5 Marks.

Section - ASingle Choice Correct (Q. No. 1 to 10)

The Questions given in this section are MCQs with four answer options (A), (B), (C) and (D) out of which ONLY ONE iscorrect. Choose the correct answer and fill the answer in the OMR sheet provided at the end.

1. Consider the circuit shown in the adjacent figure. The currentthrough the 4 resistors would be (consider all the batteriesas ideal)(A) 4.5 A

24V 24V

24V 24V

24V

24V

24V

A B C

(B) 5 A(C) 13.5 A(D) 11.5 A

2. The value of current through the 20 resistor is :

++

+

––– 10V

10V

6V

(A) 1.2 amp(B) 0.3 amp(C) 0.6 amp(D) None of these

3. An 80 µC charge is given to the 4 µF capacitor in the circuit shown inthe figure so that the upper plate A is positively charged. An unknownresistance R is connected in the left limb. As soon as the switch S inthe central limb is closed, a current of 2A flows through the 2 resistorin the central limb. The capacitive time constant for the circuit is :(A) 56 µs (B) 8 µs

R AB4µF 80µC

+–

(C) 200 µs (D) 40 µs

4. A conducting sphere A of radius rA carries a charge Q. Another conducting sphere B of radius rB is unchargedinitially. Both the spheres are separated by a very large distance. Sphere A is connected with sphere B through a longconducting wire of zero resistance through a switch S as shown in the figure. At t = 0 switch S is closed.As soon as the current flow through the wire vanishes, switch S is opened,sphere A is again charged to a total charge Q and then switch S is again closedand the process is continued for infinite times. If q is charge transferred tosphere B when the switch S is closed for the first time, then total charge on thesphere B after large number of such processes is :

Q

A B

SrA rB

(A) Q (B) qQ

Q q (C) 2B

A

rQ

r (D) None of these

5. In a spherical charge distribution, the charge density varies as (r) = 212

QR r

for R1 < r < R2, where

r is the distance measured from the centre O of the sphere as shown in the figure. A point chargeQ lies at the centre of the sphere (at r = 0). Choose the appropriate curve for variation of variationof magnitude of electric field E in the space as a function of r :

R1QO

R2

r

(A)

E

rR1 R2

(B)

E

rR1 R2

(C)

E

rR1 R2

(D)

E

rR1 R2

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6. Consider the circuit shown in the figure. Taking the potential to be zero at thenegative terminal of the battery :(A) Potential at F will be higher than the potential at C

R 2R

4R

R

RB

A

D

E

DE0

R(B) Current in AF will be greater than that in BC(C) Direction of current in CF will be from C to F(D) Current in FE will be greater than current in CD.

7. Consider the RC circuit shown in the figure. Initially the capacitor was uncharged. Ata certain instant after closing the switch it was found that the current drawn from thebattery was 3E/5R. At this instant the charge on the capacitor will be :

(A) 415CE (B) 2

5CE

A

B

R

CR

E

D R(C) 2CE (D) 5

CE

8. Two positive and two negative charges are kept in x-y plane in free space as shown in the figure.The magnitude of electric field due to the system of charges at a point P (0, y) will by (y >> d) :

(A) 30

54

qdy

(B) 30

24

dqy

dx+q–q

O

+q

–qP y(0, )

y

d(C) 304

dqy

(D) 30

34

dqy

9. The charge on the condenser of capacitance 2µF at steady state in thefollowing circuit will be :(A) 4.5 µC

+ –8V

2V+–

+–2V

2V

3µF

4µF

2µF

3µF(B) 6.0 µC(C) 7 µC(D) 30 µC

10. In the given circuit, all the capacitors are initially uncharged. After closing the switch S1 and S2 for a long time thentotal stored electrostatic energy in the circuit will be :

CEC

EC

EC

E

S1

S1

(A) 4 CE2 (B) ½ CE2 (C) 2 CE2 (D) 0

Section - BMore than one Choice Correct (Q. No. 11 to 15)

The Questions given in this section are MCQs with four answer options (A), (B), (C) and (D) out of which ONE or MOREthan ONE answers may be correct. Choose all the correct answer options and fill the answer in the OMR sheet providedat the end. You will get marks in a question only if all the answer options of that question are chosen by you.

11. Inside an electrical conductor there is a cavity and a charge Q is suspendedfixed inside the cavity space without any electrical contact with conductor. Let

1E , be the electrostatic field due to charge q at P. 2E be the electrostatic fieldat P due to induced charge on the inner surface of cavity. 3E be the electrostaticfield at P due the induced charge on the outer surface of conductor then :

Cavity

P

q

(A) 1 2 3E E E = 0 (B) 1 2E E = 0 (C) 1 3E E = 0 (D) 3E = 0

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12. A non-conducting sphere A of radius R is having a total charge + Q0 distributeduniformly over its volume. It is kept concentric inside a metallic sphere B of innerradius 2R and outer radius 3R. Whole system is kept concentric inside a metallicshell C of radius 4R. Hollow metallic sphere is earthed. Spherical shell of radius4R is given a charge +Q0 as shown in the figure. If E is magnitude of electrostaticfield and r is radial distance from the centre O of the system. Then :(A) E-r graph is non differentiable at 4 points

C B

A

Q0

Q0O

R2R 3R

4R

+ + +++

+++ + + +

++

(B) E-r graph is non differentiable and discontinuous at 3 points.(C) E-r graph is non differentiable at 3 points and it is discontinuous at 2 points(D) E-r graph is discontinuous at 3 points

13. There is a system of four large parallel plates A, B, C, and D. Plates A and Care connected to each other with the help of metallic wire and plates B andD are connected to the ground will the help of open switches S1 and S2.Distance between consecutive plates is d. Initially plates A and B are havinga charge of Q0 each and plate D is having charge +2Q0 (See figure). At t = 0switches S1 and S2 are closed simultaneously. Then the magnitude of chargeflown through switch :(A) S1 is 5Q0 / 3 (B) S1 is Q0

d d d

+Q0+2Q0+Q0

A B C D

s1 s2(C) S2 is 7Q0 / 3 (D) S2 is 2Q0

14. For the circuit shown in the figure :R1 R6

R5R3

R4

R2

A

B

C

F

E

D

(A) Equivalent resistance between G and C is independent of R5 & R6.(B) Equivalent resistance between G and C is dependent only on R1, R2, R3 & R4.(C) Equivalent resistance between E and A is independent of R3.(D) Equivalent resistance between D and G is independent of R1, R2, R3, R4, R5, R6.

15. A charge particle of mass m and charge q is at rest due to the horizontalinfinite non-conducting charged sheet as shown in the figure. If r isvery small, then :

(A) Charge density of plate = 02mgq

mq

r

(B) If charge particle is slowly displaced & released, it will still remainat rest in the new position.(C) If charge particle is displaced by a small distance then the motion of charge particle is oscillatory.(D) If charge particle is given a velocity v0 parallel to plate then it is continuously move along the same direction withsame velocity.

* * * * *

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OMR Sheet for the PG Brainstormer - 1C

123456789

10

1112131415

A AB BC CD D



Time Allowed 45 Min

Maximum Marks 55

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ANSWER KEYSection - A

1. (C) 2. (C) 3. (D) 4. (B) 5. (B) 6. (A) 7. (D) 8. (A) 9. (B)10. (C)

Section - B

11. (A) (B) (D) 12. (A) (D) 13. (A) (C) 14. (A) (B) (D) 15. (A) (B) (D)



Time Allowed 45 Min

Maximum Marks 55

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PG Brainstormer - 1C