# Free Objective Test 01 Practice Test - 11th and 12th

### Question 1

In an adjoining figure are shown three capacitors C_{1},C_{2} and C_{3} joined to a

battery. The correct condition will be (Symbols have their usual meanings)

#### SOLUTION

Solution :C

Q

_{1}=Q_{2}+Q_{3}because in series combination charge is same on both thecondenser and V=V

_{1}+V_{2}because in parallel combination V_{2}=V_{3}Hence V=V

_{1}+V_{2}

### Question 2

If two conducting spheres are separately charged and then brought in contact, then

The total energy of the two spheres is conserved

The total charge on the two spheres is conserved

Both the total energy and charge are conserved

The final potential is always the mean of the original potentials of the two spheres

#### SOLUTION

Solution :B

The total charge on the spheres will be conserved

### Question 3

In a charged capacitor, the energy resides** **as

Positive charges

Both the positive and negative charges

The field between the plates

Around the edge of the capacitor plates

#### SOLUTION

Solution :C

In a charged capacitor energy is stored in the form electric field

### Question 4

The insulated metal spheres of radii R_{1} and R_{2} having charges Q_{1} and Q_{2} respectively are connected to each other. There is ** **

No change in the energy of the system

An increase in the energy of the system

Always a decrease in the energy of the system

A decrease in the energy of the system unless Q_{1}R_{2}=Q_{2}R_{1}

#### SOLUTION

Solution :D

When Potentials of spheres are unequal, current will flow in connecting wire so that energy decreases in the form of heat through the connecting wire.

### Question 5

When a dielectric slab is introduced between the plates of an isolated charged capacitor, it

Increase the capacitance of the capacitor

Decreases the electric filed between the plates

Decreases the amount of energy stored in the capacitor

All of the above

#### SOLUTION

Solution :D

As the capacitor is isolated, the potential decreases as the capcitance increases

### Question 6

A conducting sphere of radius R, and carrying a charge q is joined to a conducting sphere of radius 2R, and carrying a charge – 2q. The charge flown between them will be?

#### SOLUTION

Solution :D

Initial charge on sphere of radius R = q

Charge on this sphere after joining =q′=Rq+(−2q)×RR+2R=−q×R3R=−q3

So charge flown between them =q−(−q3)=4q3

### Question 7

A parallel plate air condenser has a capacity ‘C’. When the plate separation is halved and a dielectric of constant k is inserted, new capacitance is found to be 12C. The value of dielectric constant ‘k’ is?

#### SOLUTION

Solution :C

C=ϵ0Ad;C1=kϵ0A(d2)

C1C=2k;

12=2k; k=122=6

### Question 8

A certain number of identical condensers are first connected in series and then in parallel. If the equivalent capacities in the two cases are found to be in the ratio 1: 9, what is the number of condensers?

#### SOLUTION

Solution :B

CseriesCparallel=(Cn)nc=1n2

19=1n2

n=3

### Question 9

In the circuit given below potential difference across 6 μ F capacitor is

#### SOLUTION

Solution :B

q=C1V1=C1V2

V1V2=C1C1=94.5=21

V1+V2V2=2+11

V2=123=4V

### Question 10

A capacitor 1mF withstands a maximum voltage of 6KV, while another capacitor 2mF withstands a maximum voltage of 4KV. If the capacitors are connected in series, the system will withstand a maximum voltage of?

#### SOLUTION

Solution :D

q1=C1V1=10−3×6×103=6C

q1=C2V2=2×10−3×4×103=8C

Q=q1=6C Q=CV

6=(C1C2C1+C2)V

6=23×10−3V

V=9×103V

=9KV

### Question 11

A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by Δ T, the potential difference V across the capacitance was?

#### SOLUTION

Solution :D

12CV2=mSΔT

V2=2mSΔTC

V=√2msΔTC

### Question 12

If in the infinite series circuit, C = 9 μF and C1=6μF then the capacity across AB is

#### SOLUTION

Solution :C

1CAB=1c+1c1+x+1c

1x=19+16+x+19

1x−16+x=29

6+x−xx(6+x)=29

27=x(6+x)

x=3μF

### Question 13

The capacity of each condenser in the following fig. is ‘C’. Then the equivalent capacitance across A and B is?

#### SOLUTION

Solution :C

CAB=22c3=4c3

### Question 14

The radii of two charged metal spheres are 5 cm and 10 cm both having same charge 75 mC. If they are connected by a wire, the quantity of charge transferred through the wire is

#### SOLUTION

Solution :A

V=q1+q2C1+C2=q1+q24πϵ0[r1+r2]=150×10−3×9×10915×10−2

V=9×109V

q11=C1V=4πϵ0 r1×9×109=19×109×5×10−2×9×109=5×10−2C

q11=50mc

q1−q11=75−50=25mC

### Question 15

A parallel plate condenser of capacity 5 μ F is kept connected to a battery of emf 10 V. If the space between the plates is filled with a medium of dielectric constant 12, then the additional charge taken from the battery is?

#### SOLUTION

Solution :D

q1=c1V=5×10−6×10=50μc

q11=kc1v=12×5×10−6×10=600μc

Add. Charge=q11−q1=600−50

=550μC