nkhwl;Lit gy;fiyf;fof nghwpapaw;gPl jkpo; khztu;fs;

elhj;Jk; fh.ngh.j cau;ju khztu;fSf;fhd

gapw;rpg; guPl;ir - 05

ngsjPftpay;

Gs;sp toq;Fk; jpl;lKk;

gy;Nju;T tpdhf;fSf;fhd tpsf;fTiuAk;

gy;Nju;T tpdhf;fSf;fhd tpilfs;

Q Ans Q Ans Q Ans Q Ans Q Ans

01. 1 02. 4 03. 3 04. 1 05. 5

06. 1 07. 3 08. 2 09. 4 10. 2

Gs;spj;jpl;lk;

gFjp 𝑰 = 𝟏𝟎 × 𝟐 = 𝟐𝟎 Gs;spfs;

gFjp 𝑰𝑰 = 𝟓𝟎 Gs;spfs;

gFjp 𝑰𝑰𝑨(mikg;Gf;fl;Liu tpdh)= 𝟏 × 𝟐𝟎 = 𝟐𝟎 Gs;spfs;

gFjp 𝑰𝑰𝑩(fl;Liu tpdh)= 𝟏 × 𝟑𝟎 = 𝟑𝟎 Gs;spfs;

nkhj;jk; = gFjp 𝑰 +gFjp 𝑰𝑰

= 𝟐𝟎 + 𝟓𝟎 = 𝟕𝟎 Gs;spfs;

= 𝟕𝟎

𝟕𝟎× 𝟏𝟎𝟎 = 𝟏𝟎𝟎 Gs;spfs;

gy;Nju;T tpdhf;fSf;fhd tpilfSf;fhd tpsf;fTiufs;

(1) ce;jk;Neuk; =

kgms-1

s = kgms-2

,J tpirapd; myF / tpil (1)

(2) 1

sinc = ng

n1

600 > c

sin600 > sinc

√32 >

nl

ng

(3) myF ePsj;jpzpT m vd;f.

rkepiyf;F>

F+amg sinα =bmg

μamg cosα + amg sinα =bmg

cuha;Tf;Fzfk; =μ= tanα

tanα.amg cosα + amg sinα =bmg

2amg sinα =bmg

2 sinα =ba

(4) RtUf;Fk; mjpupf;Fk; ,ilapy; epd;w miy fhzg;gLk.; mKf;f tpj;jpahrk;

Kuz;fZtpNy ,opthf ,Uf;Fk;.

λ = 4×3 =12m

f = 36012 =30Hz

mbg;G kPbwd; 5Hz vdNt B ,d; kPbwd; 25Hz or 35Hz

/ tpil 25Hz

(5) =3×105 Jkg-1×3kg

60×60 s = 1000 Js-1

4 =250 Js-1

(6) p = hpg Mok; $l mKf;fk; $Lk;.

(7)

R5 w;F FWf;Nf 3V NtWghL / R5 ,D}lhf 0.5A nry;Yk; /R3 ,D}lhf 3.5A k; R4 ,D}lhf 0.5A k; nry;Yk;

/(A,B) w;F ,ilapyhd tpisAs; jil 134 Ώ

/bulb ,d; jil 133 Ώ

(8)

θ1>θ2 θ1> θ >θ2

Q= 𝐾𝐴(𝜃0−𝜃𝑙)

𝑑

AK1(θ1-θ)

d = A K2(θ-θ2)

d

K1θ1 – K2θ = K2θ- K2θ2 K2θ2 + K1θ1 = (k1+k2) θ

Θ =(K2θ2 + K1θ1)

(k1+k2)

CV = CVo + CVo

2 ⟹ V =3Vo

2 (9) (A)

Vo = 2V3

(B) CV = CVo+2CVo

Vo =V3

(10) nrdu; ,Uthap gpd;Kff; Nfhlypy;>

V2 = 12V , Imax =30mA cU(3) ,y; fhl;bathW Vi khWk; NghJ Vi ,d; kpff;$ba ngWkhdj;jpd;

NghJ jil R ,d; ngWkhdk; fhzNtz;Lk;. Vi(max) =13.5V

Mdhy; V2 = 12V / VR = 1.5V Mdhy; Imax =30mA

vdNt R = VI =

1.5V30mA =50Ώ

/ tpil (2)

mikg;Gf;fl;Liu tpdhtpw;fhd tpilfs; (1)

(a)

1.

....(4) Gs;spfs; (G+uzkhd tpilf;F)

2. M = 𝑓𝑜

𝑓𝑒 ………………….…. (1) Gs;sp

(b)

1.

………………….…. (4) Gs;spfs;

2.

(1) S Fwpj;jy; ………………….…. (1) Gs;sp

(2) kw;iwa nghUl;fspypUe;J tUk; xspf;fjpu;fis jtpu;f;f / P1 ,d; tpk;gj;ij

njspthf Nehf;Ff. ………………….…. (1) Gs;sp

3.

(1) gad;gLj;j Ntz;ba Crp P2 ………………….…. (1) Gs;sp

P2 I njspthf Fwpj;jy;. ………………….…. (1) Gs;sp

(2) fz; ,aq;Fk; NghJ P1 ,d; tpk;gKk; (X') P2 ck; rhu;gpaf;fk; mw;w epiyapy;

ngWjy;. ……………….. (2) Gs;spfs;

1/v

1/u

4.

……………….. (2) Gs;spfs;

(c)

1. FopTtpy;iy ………………….…. (1) Gs;sp

2. 1

𝑣−

1

𝑢 =

1

𝑓 ⇒

1

100−

1

∞ =

1

𝑓 ………………….…. (1) Gs;sp

f = 100 cm ………………….…. (1) Gs;sp gad;gLj;j Ntz;ba tpy;iyapd; FtpaePsk; 100 cm

(𝟐𝟎 Gs;spfs;)

fl;Liu tpdhtpw;fhd tpilfs;

1) a)

i) kpd;Gyk; xd;wpYs;s xU Gs;spapy; itf;fg;gl;l XuyF NeNuw;wj;jpd; kPjhd Njwpa kpd;tpir

………………..(01 Gs;sp) ii) mk; kpd;Gyj;jpy; kpd;Gyr;nrwpT JHuj;Jld; khwhJ.

………………..(01 Gs;sp) iii) Neu;>kiw Vw;wg;gl;l jl;Lf;fis xd;Wf;nfhd;W rkhe;jukhf itg;gjd;

%yk; (Fwpj;j ,ilntspapy; ) ………………..(01 Gs;sp)

b) i)

……………….(02 Gs;spfs;)

+ _

ii)

……………….. (02 Gs;spfs;)

iii) mq;F fl;lhak; Vw;wk;> Fwpj;j mOj;jNtWghL fhzg;gl Ntz;Lk; ………..(01 Gs;sp)

c) ∅𝐸 =𝑄

∈

………………..(01 Gs;sp) ∅𝐸 = 𝐸𝐴 ……………….(01 Gs;sp) i)

1) r>R

E× 4𝜋𝑟2 = (𝑝 ×4

3𝜋𝑅3)

1

𝜖0 ………………..(01 Gs;sp)

𝐸 =𝑝𝑅3

3 ∈0 𝑟2

2) r=R

E× 4𝜋𝑟2 = (𝑝 ×4

3𝜋𝑅3)

1

𝜖0

………………..(01 Gs;sp)

𝐸 =𝑝𝑅3

3 ∈0 𝑟2

𝐸 =𝑝𝑅

3∈0 ∵ (𝑟 = 𝑅)

………………..(01 Gs;sp) 3) r<R

E× 4𝜋𝑟2 = (𝑝 ×4

3𝜋𝑟3)

1

𝜖0

………………..(01 Gs;sp)

𝐸 =𝑝𝑟

3∈0

………………..(01 Gs;sp)

4) ………………..(01 Gs;sp)

E

R

𝑝𝑅

3 ∈0

r

-

……………….. (01 Gs;sp)

5) v =Q

4π∈0r

v =𝑝 ×

43𝜋𝑅3

4π ∈0 r , v =

𝑝𝑅3

3 ∈0 r

ii)

1) r>R

E× 4𝜋𝑟2 = [4

3𝜋𝑎3𝑝 +

4

3𝜋(𝑏3 − 𝑎3)(−𝑝)]

1

𝜖0 ………..(01 Gs;sp)

𝐸 × 4𝜋𝑟2 =4

3𝜋

𝑝

∈0(2𝑎3 − 𝑏3) , 𝐸 =

𝑝(2𝑎3 − 𝑏3)

3 ∈0 𝑟2

2) a<r<b

E× 4𝜋𝑟2 = [4

3𝜋𝑎3𝑝 +

4

3𝜋(𝑟3 − 𝑎3)(−𝑝)]

1

𝜖0 ………….. (01 Gs;sp)

𝐸 =𝑝(2𝑎3−𝑟3)

3∈0𝑟2

……………….(01 Gs;sp) 3) r<a

E× 4𝜋𝑟2 =4

3𝜋(𝑎3 − 𝑟3)𝑝

1

𝜖0

………………..(01 Gs;sp)

𝐸 =𝑝(𝑎3 − 𝑟3)

3 ∈0 𝑟2

iii) 1)

i) 𝐸1 =

𝑝𝑟1

3∈0

………………..(01 Gs;sp)

ii) 𝐸2 =

−𝑝𝑟2

3∈0

………………..(01 Gs;sp)

iii) 𝐸 = 𝐸1 + 𝐸2

………………..(01 Gs;sp)

�� = 𝑝𝑟1

3∈0

+ −𝑝𝑟2

3∈0

=𝑝

3∈0(𝑟1 − 𝑟2 )

= 𝑝

3∈0(𝑋𝑍 − 𝑌𝑍 )

………………..(01 Gs;sp)

=𝑝

3∈0(𝑋𝑍 + 𝑍𝑌 )

………………..(01 Gs;sp)

=𝑝

3∈0(𝑋𝑌 )

=𝑝𝑑

3∈0 ………………..(01 Gs;sp)

(𝟑𝟎 Gs;spfs;)

****************

a

b +p

-p

……………….. (01 Gs;sp)

……….. (01 Gs;sp)

……………….. (01 Gs;sp)