16

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16

16.1 )*+,,- (electric current) 6789:8);,,-<9:=>? 89:?:6<++: 8<> 8);,,-? :8+@ A<,,- >B .?<<) C;<)>7+: ;) C*D<)C::6<+A<::<E: +*D<)C::6<+8);C<<E: >779:;88=>F):6<+>7+: ;8<9::);;:6<+8); D<<)8>:6<+A<>B . 6)*+,,-7<<) )*+,,-<<)>< 67<:>+>7 )8=>967<<) 6<+>78 89:>F,,-):6<+>7+:> );;)G )*+,,-;)8 G=:6)*+,,-<=>?:=:9:=:+*<?6,,- 88=>F=<:< 9: *<?6?68=>F,,-)<>7+::=>? :B=<:< ?6)*+,,-<D=>?=<:< * *C==: G,H 9:?6,,-A= 16.1.1 ?,,- 6789:8)*+,,-=><I *<)=><>7 =>?,,- ?,,-<) <)A=>?,,- 9:;8:6<=::6+) (free electron)K;)<;:)=:8 *<)8<9::)CC886*: <9:*CCCF (Brownian motion) >>78EH<::6<=::6+) *=<)=>;ABF

:6<+8); :6<+A<

B .

B .

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89:?<>7+::*<)88=>F ;)6+8,,-@*<)>7 *9:;+8,,- ;)?:6<=::6+)<9: 88EH<8ABF 9:88E<:<9: (drift velocity) ?8)*+,,-*<) >>7 )*+,,-<);6;<9:::6<=::6+) 16.1.2 9:;)*+,,- =><I 6;<9:::@8);,,- * :6<=: :::C :::<C ;? *<)6:)*+,,->7 :)*+,,- 8>C 68Q);,,- D 97@=> :=><< A68Q+<F 8AB<:8CF =:6 9:*:8*F (A) I = )*+,,-=>< (A) Q = 68Q);>78 (C *<)<C) D@=>:=>< (C)

t = <);<9:D@=> (s) 6:)*+,,- W I X 86>C6:+8,,- W E X 1

G8)*+,,- 1.25 *:8*F +<<)+ );>78D 97 =>:+<<) +>7< 5 6 ;)8

I =

<9:*CCCF ::6<=::6+)*<) G888=>F,,- (VA = VB)

:6<=::6+)<9:8E<:<9: 89:<+::*<)88=>F,,- (VB > VA) 6)*+,,-*<)

97@=>

:@8);,,-

VA = VB

VA VB

VB > VA

VA VB

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2

G=:+<<) >C*C==: _8)*+,,-D+<7 3.2 *:8*F ;;?:6<=::6+) D 97 => :<<)>7< 5.0 6 (:6<=:8);,,- 1.6 X10-19B<:8CF) " 89:=:=>?<)>C*C==: ;)8)*+,,-=>?<) K6;<9:::6<=::6+) >B 6;Q=>?<)

s = vt

I = 1.25 A

I I

I = 3.2 A

89: t = 5 , Q = ?

;)*+,,- I =

Q = It = 1.25x5.0 Q = 6.25 C Ans

;)*+,,- I =

Q = It Q = 3.2x5.0 C *=:6<=: 1 =>8); 1.6 X10-19 C ;)8;?:6<=: = ..

.

= 1x1020 => Ans

I E

)*+:6<=:

+8,,- , ;)<9:=8>C E

)*+,,-=>?<) (I) ;)86=8>C6<9:::6<=::6+)9:)*+:6<=:

www.schoolDD.com 4

;68)*+,,- I = *<));,,- Q = Ne = (nAs)e = (nAvt)e = nevtA

>>7 I =

I = nevA n = 8*::6<=::6+) (:@ / m3) e = );::6<=: (1.6 x 10- 19 C) v = 8E<:<9:::6<=: (m/s) A = 97@=><=>? (m2) 3

<+8:6<=::6+) 5.0 x 1028 =>=:<CF8= <8 97=> 2.5 =86<<68= G:6<=:*=<)=><9: 8E<:<9: 0.30 86<<68==:6 ;)8)*+,,-+<7 16.2 &' '()* (I) &'-.* (V)

16.2.1 012"2*' &'3 )*+,,-D<<) 8*D>=>C8=>F,,-)<>7+::<<) I V I = KV (89: K = :*D>)

=

= R (89:

= R)

89: R = 8= 8A<=F =:*:8*F 9::F8 ( Ω )

V = I R n::F8 9:

A = 2.5x10-6 m2

n = 5x1028 v = 0.3x10-3 m/s

I = ? ; I = nevA = 5x1028x1.6x10-19x0.3x10-3x2.5x10-6 I = 6.0 A Ans

;.:6<=:

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- 89::Q@B86=> H )=>?<)>7 88==> *<)A=8n::F8

4

,8+>8 >oF)8=>F*<))*+,,- A>B ;8=:=>= 5

;)=:=:=>= 1.0 8):F8>C8=>F ;;)8)*+,,- 1.0 86<<6*:8*F D=>=>< 3 (Resistor) =>= A:QF>C8=>C; 9:>C)*+,,- 9:8=>F,,- :8)>C;>7I =>=8 2 *CC 9: 1. 3& (Fixed resistor) ?;DFC::>*AB)C:<EI 88==> +><>QF ;,,- *<)*GC+C:8=

<)

V

I

<::

V

I

:6<<=F

V

I

+=>?

V

I

3 2 1

0 0.2 0.4 0.6 I (A)

V (V)

;n::F8 V = IR = 1x10-3x1x106

V = 1x103 V Ans

V = ?

I

R = 1x106 Ω

I = 1x10-3 A

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*GC+ *GC 1 *GC 2 *GC 3 *GC 4 *< *< BQ 8<<9: ? 0 0 1 - 7?=< 1 1 101 1 % * 2 2 102 2 % +8 3 3 103 - <9: 4 4 104 - 5 5 105 - 7?6 6 6 106 - 8 7 7 - - 8 8 - - 9 9 - - : - - 10-1 5 % 6 - - 10-2 10 %

2. 3=& (Variable resistor) A=>=+8G>C8= 8 : 9:C868Q)*+,,-; =>=* ):C*GC8= K:;?*,=F 9:< >=:>C 1 *<)3 *<)+>8D>+ =:>C 2 +><>QF ;,,- "2 (Diode) : A:QF6;:6<:6+F>I?;+=>?+><>QF ;,,- :8>7,,-C *<)>7,,-<C =::;,,-8 2 *CC9:

*:886=:F

2

=>=*

3 1

*C==:

A

*:886=:F

:

I

*C==:

A *:886=:F

:

88)*+

*C==:

A

8=;) 68789:<9:+>8D>+ 2 ;=?* 1 >=?* 3 *<)G<9:6=88=;)<<

=:*CCC*:+= 8)*+,,-; =:*CCC*:++<>C88)*+,,-;

*GC+ 4 *GC C=>= 888>7 *GC 1 C:<=>* *GC 2 C:<=>+: *GC 3 C:<?<>?BQ>C <+: =>* *GC 4 C:8<<9:A:<) =>=>B 8*GC+ 7?=< +8 *<)* ;)88= 15x103 :F8 *<)88<<9: 2 % 9:>C 15,000 :F8 300 :F8 9:8) 14,700 :F8 G 15,300 :F8

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- ::8)*+,,-D6 ;:*<,,-)*++<>C A,,-)*+= 6

=>= a 8*GC++8? * *<): =>= b 8*GC+ 7?=< +8 *<)6 *<)=>= C 8*GC+ 7?6 <9: *<): =>=*=<)=> 88=

=>= a 88= = 30x102 Ω 150 Ω

=>= b 88= = 18x103 Ω 1800 Ω

=>= c 88= = 16.2.2 B(3 B(

B(3 WX A+8C>=6H ):+6I +=6> ;)8+@ =,,-=> +6>+@ =;)87:B>C:Q@B86:+>< +@ =,,-8A:F88= ;8+>8 >oF)8=>F,,- (V) *<))*+,,- (I) 9:8=:<<) (R) 8<=I> C

ℓ

9: R ℓ

=>: 6 = 1.6x10

-8 Ω m , :* = 1.7x10-8 Ω m

* = 1010- 1014 Ω m , K = 10

14- 1018 Ω m

7

<:*+8?+8: +<) 10 8= +8+DBF< 1 86<<68= :+8+DBF< 2 86<<68= 8= :<*=<)+A *<)CC8= :<>7+:+ (? :* = 1.7x10

-8 Ω m)

1 8 103 10%

3 0 102 5%

R =

+8 ? * :

7?=< +8 6

7?6 <9: :

8<<)

.=><<)

>>7 89: 9:=> 9:+@ =,,-

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+* 8=;

R = !ℓ

R1 = ."#

".$%

R1 = 0.216 Ω Ans ++: 8=;

R = !ℓ

R2 = ."#

.&'

R2 = 0.054 Ω Ans

CC (() = .

.& = 4

<:* 1 86<<68= 88=8 2 86<<68= :B 4 Ans &' CGE A+<>C:8=,,- 8A(:F8)-1 9: K8+F (S)

G = (

B( C*E A+8C>=6H )=>:+ *<)A+<>C:+@ =,,- 8A (:F88=)-1 9: K8+F=:8= (S/m)

* = !

16.2.3 G122HIBJ''2&'3

K A+8+@ =+B8 * K 89: T 68 ---> R << L 8+@ =:B)=>? *<)H K6<6: *,=F 89: T 68 ---> R << A+8+@ ==? 6 :* * <6>8 89: T 68 ---> R 687

A = +,)

& = .&-./)

& = 7.85x10-7 m2

d = 1x10-3 m ℓ = 10 m

A = +,)

& = .&-./)

& = 3.14x10-6 m2

d = 2x10-3 m ℓ = 10 m

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B(.. (Superconductivity) 8G +@ +8+@ =,,-ABF ( = 0) :Q@B86*<):Q@B867 2HIBJ'S (critical temperature) *<)>+ 9:+7 ..(Supper conductor)

16.3 (T

16.3.1 &U2 ( E) &'-.* (V) 89:=:*<?6,,- (G,H *C==:) >C=>= <:, C; 8)*+,,-<D=> = *<)*<?6 )*+,,-679:; <9::);,,-9::6<=:>C <> ;*<?6,,->B 89: 6;Q;):C=>=88= R =:>C*C==: 8*<9:,,- E *<)88=@ r K8: )*+,,- I ;)D>7=>= *<) *C==: >B <>,,-;*<?6,,- (*C==:) <:::8;)8);,,- Q BQ>C* <9:,,- E *<)GB89:D=>= r *<) R K8>C );,,- Q BQ>C8=>F)<:=>=>7+: WE = <>,,-;*<?6 WR = <>,,-D=>= R Wr = <>,,-D=>= r ;n:>F <>;) WE = WR + Wr QE = QVR + QVr

;)

I

*<?6,,-

E I

=>= R

I

VR

r E V

Vr

R

I

E = VR + Vr

:6<=:6+>C I

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9: E = IR + Ir

;) I = 0

-(12/

;B; G V 9:8=>F)>7*C==: ;) V = VR *<) G> V 888= R =::B< ;) V 3 E G9: V = E 8

*C==:: 8*<9:,,- 12.0 <=F *<)8=@ 2.0 :F8 =:>C=>= 7.0 :F8 ;8=>F)>7:*C==: ?Q7 ;)*==>C><=F86=:F 88=+B8 88=>==::B9:8 )= I ; E = VR + Vr E = IR + Ir

I = 0

-(12/ =

-"1/ =

A

;B V = VR = IR

= x70

V = 11.67 V Ans G888==:

;) V 3 E = 12 V Ans

VR

r = 2 E = 12 V V = ?

Vr

R = 20 Ω

I

r = 2 E = 12 V V = ?

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16.3.2 ( 6;Q;,,->B Q = );,,-<9:D=>=< t (C) I = )*+,,-D=>= (A) V = 8=>F:=>= (V) W = <>,,-=>= ( J)

; I = 9: Q = It *<) V = IR

W = ItV = I2Rt = )

(

C P E 8G <>,,-< 8A ;B<=:6 9:>==F (W) 9

*C==:*:<<F 1.5 <=F 2 : *CC:8 ?+8G;)*+,,- 20 86<<6*:8*F >C6<E 20 >8 G*C==: :<) 15 C ;,,-=: <>,,- 1 <>,,-6 ; W = QV = ItV

E

I

R

I V

W = QV

P = 4

>>7

P = 5 = ItV

= IV

6

E = 1.5x2 = 3 V

t = 20 hr I=20 mA

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= 20x10-3x(20x60x60)x3 W = 4320 J

,,-=: <>,,- 1 = &

= 0.007 C/;B< Ans

16.4 23 2

16.4.1 23

1. 22H' A=:?=>= 8=:>:B+>>B =:*CC:8>B+ - )*+,,-D=>==>> I = I1 = I2 = I3 - 8=>F,,-8 = D<88=>F,,-: V = V1 + V2 + V3 ; V = V1 + V2 + V3

*<) V = IR (_::F8) >>7 IR8 = I1 R1 + I2 R2 + I3R3 89: R8 = 8=8: R 1 , R 2 *<) R 3 2. 21 A=:?=>=<I=> 8=:8A<8>B

R3 R1 R2

I1

E

I V

V1

I2 I3

V2 V3

R' = R1 + R2 + R3 (I = I1 = I2 = I3)

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=:*CC>B+ - 8=>F=:8=>=*=<)=> = 8=>F,,-8 V = V1 = V2 = V3

- )*+,,-D>78 = D<8:)*+,,-D=>=*=<)=> I = I1 + I2 + I3 ; I = I1 + I2 + I3

*<) V = IR 9: I = (

>>7 (8

= ( + )

() + .

(.

89: R8 = 8=8: R1 , R 2 *<) R3 - =:=>=*CC:8 8=8;)8 8=8Q=:*CC ?)*+,,-; =:=>=*CC:8 8: )*+,,-; =:=>=*CC

- =:=>=*CCD+8 A=:=>=*CC:8 >C=:*CC 10

;B8=8889: . +6=F S | . +6=F S |

E

V1 = V2 = V3

R3 I I

I1

V

I3

R2 I2

R1

9

:8 =

9

:9 +

9

:; +

9

:< (V = V1 = V2 = V3)

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. +6=F S | ;>B*CC8;) 8= R 1 *<) R 2 =:>*CC:8 ;)8=8 R 12 = R 1 + R 2 = 1 +2 = 3 Ω 8= R 3 *<) R 4 =:>*CC:8 ;)8=8 R 34 = R 3 + R 4 = 3 +4 = 7 Ω B8>7 ;B8= R 12 *<) R 34 =:>*CC

;)8=8 (8

=

() +

(.= =

+

" =

"1

(8 =

R8 = 2.1 Ω Ans . +6=F S | ;>B*CC8;) 8= R 1 *<) R 3 =:>*CC

4 Ω 3 Ω

2 Ω

B S

1 Ω

I

A

R4 R3

R2 R1

4 Ω 3 Ω

2 Ω

B

1 Ω

I

A

R34

R12

7 Ω

B

3 Ω

I

A

R4 R3

R2 R1

4 Ω 3 Ω

2 Ω

B

1 Ω

I

A

www.schoolDD.com 15

;)8=8 (.

=

( +

(. =

+

=

1

(. =

&

R13 =

& Ω

8= R 2 *<) R 4 =:>*CC

;)8=8 ()=

=

() +

(= =

+

& =

1

&

()= =

&

R24 = &

Ω

B8>7 ;B8= R 13 *<) R 24 =:>*CC:8 ;)8=8 R8 = R13 + R24 =

& + & = > 1

=

R8 = 2.08 Ω Ans 16.4.2 22

1. 22H' A=:?>7=8:*C==: 8=:>:B+> =:*CC=:*CC:8;) - *<9:,,-8 = D<8:*<9:,,-: 8=@8; =:=>=*CC:8

R24 R13

4/3 Ω B 3/4 Ω

I

A

E3 r1 E1

R

I

r2 E2 r3

E' = E1 + E2 + E3

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2. 21 A=:?>76>:*C==:*=<):8=:> 89:*<9:,,-:*C==:*=<):> E1 = E2 = E3 ;)+=:*C==:*CC - *<9:,,-8 = *<9:,,-::*C==:*=<): - 8=@8;=:=>=*CC - =:*C==:*CC:8 ;)*<9:,,- 687 +=:*CC*<9:,,-;)>

68 11

89:?*C==: 89:>+:: 8=:*CC:8;)8)*+,,- 0.25 *:8*F D=>= 8:F8 G=:*C==: *CC ;)8)*+,,- 0.16 *:8*F ;*<9:,,- *<)8=@*C==: *<9:,,- *<)8=@ :*C==:*=<):>C E *<) r =8<?>C

r' = r1 + r2 + r3

E' = E1 = E2 = E3

9

@8 =

9

@9 +

9

@; +

9

@<

E3

r2 E2

R

I r1 E1

r3

www.schoolDD.com 17

=:*CC:8 *<9:,,-8 E8 = E1 + E2 = E + E = 2E *<)8=@8 r8 = r1 + r2 = r + r = 2r B8;) ;B V = E8 I r8 *<) V = IR ;) IR = 2E I(2r) 0.25x8 = 2E 0.25(2r) E 0.25r = 1 ---1 =:*CC *<9:,,-8 E8 = E1 = E2 = E

*<)8=@8 28

=

2 +

2) =

2 +

2 =

2

r8 = 2

B8;)

r1 E1

R = 8 Ω

I = 0.25 A

r2 E2

V

V r8 E8

R = 8 Ω

I = 0.25 A

r1 E1

R = 8 Ω

I = 0.16 A

r2 E2

V

V r8 E8

R = 8 Ω

I = 0.16 A

www.schoolDD.com 18

;B V = E8 I r8 *<) V = IR ;) IR = E I(2

)

0.16x8 = E 0.16(2)

E 0.08r = 1.28 ---2 2-1, -0.08r + 0.25r = 0.28 0.17r = 0.28 r = 1.7 Ω Ans * r 2 ;) E 0.08(1.7) = 1.28 E = 1.41 V Ans

16.5 &*T U]23 ?n 97,,- n:>F <> n:>F);,,- =:=>= *<)=:*C==: 8)=F;,,- 97 12

;)*+,,-D=>= a , b *<) c ;,,->B ? E1 = 6 V , E2 = 6 V , r1 = 1 Ω , r2 = 1 Ω , Ra = 7 Ω , Rb = 4 Ω , Rc = 12 Ω 6;Q=>= =>= b *<) c =:> *<=::8>C=>= a

8=8: b >C c (AB

=

(A +

(B =

& +

= 1

= &

=

Rbc = 3 Ω 8=8: a >C bc R8 = Ra + Rbc = 7 + 3 R8 = 10 Ω 6;Q*C==: *C==: E1 *<) E2 =::8> *<9:,,-8 E8 = E1 + E2 = 6 + 6 = 12 V

c

r1 E1

a

I r2 E2

b

www.schoolDD.com 19

8=@8 r8 = r1 + r2 = 1 + 1 = 2 Ω B8;) ;B V = E8 I r8 *<) V = IR8 ;) IR8 = E8 I r8 Ix10 = 12 Ix2 I = 1.0 A )*+,,-D=>= a , Ia = I = 1.0 A Ans ;)B68;) Ia = Ib + Ic 1.0 = Ib + Ic Ic = 1.0 - Ib *<) Vb = Vc IbRb = IcRc IbRb = (1.0 - Ib)Rc Ibx4 = (1.0 - Ib)x12

Ib =

=

& = 0.75 A Ans

*<) Ic = 1.0 - Ib = 1.0 - 0.75 = 0.25 A Ans 13

:<*+=> ;)<*+89:8)*+,,- 10 86<<6*:8*F DQ)=:C*:+= *<)8=>F)>7 1.2 <=F G?:=>7 =:>C*C==: 6 <=F 88=@:8 ;)=:?=>= 8=:: 9:8:+ G: =:C*:+= >C*C==: :;)+ 9:;*C==:8*<9:,,- 6 V.K+B 8=>F)>7:::89: 1.2 V.>>7;)8)*+,,-D:8 10 mA.

V r8 E8

R8

I

www.schoolDD.com 20

0

*=:*C8=>F 9:<9:8=>F >7::=8??8= R 8=::8>C:>B ;B V = VR + VD *<) V = E I r = E ;) E = VR + VD VR = E VD = 6 1.2 VR = 4.8 V 6;Q=>= ; VR = I R

R = C = &.$

.

R = 480 Ω Ans

14

;,,->B 8)*+,,- 2 *:8*F D=>= G868=@ *C==: ; . )*+,,-D<:, .8=>F)<:=>= . 8=:<:, . <>,,-GB 10 6 ;. ?<>,,-+B+=>= . )*+,,-D<:, ;)>C)*+,,-D=>= )=:>*CC:8 I<:, = I = 2 A Ans

VD VR

:<*+ V E , r = 0

R

I

r = 0

<:, E = 6 V

R = 0.5 Ω

R1

I = 2 A

www.schoolDD.com 21

. VR = ? ;n::F8 V = I R VR = 2x0.5 VR = 1.0 V Ans . R1 = ? ;B E = I r + I R + I R1 6 = 2x0 + 2x0.5 + 2xR1

R1 = D

R1 = 2.5 Ω Ans . W = ? 89: t = 10 s ; W = QV = QE

= ItE (I = )

= 2x10x6 W = 120 J Ans ;. PR = ? ; W = QV

*<) P = 5

>>7 P = QV

PR = QVR = It-IR/

= I2R = 22x0.5 PR = 2 W Ans

15

;>B *<) ;8=>F); a *<) b

R3 = 2 Ω R2 = 2 Ω

b

B .

E = 9 V

R1 = 1 Ω

a

I

R2 = 2 Ω

b B .

E = 9 V

R1 = 1 Ω

a

I

www.schoolDD.com 22

0

0

B . V2 = ? V2 ; V2 = I R2 B R2 I 8 R1 >C R2 ;) R8 = R1 + R2 = 1 + 2 = 3 Ω ; V = I R *<) V = E I r ;) E = I R8 9 = Ix3 I = 3 A V2 = I R2 = 3x2 V2 = 6 V Ans B . V2 = ? R2 *<) R3 =:>

8=8 (GA

=

() +

(. =

+

Rab = 1 Ω R1 *<) Rab =::8> 8=8 R8 = R1 + Rab = 1 + 1 = 2 Ω ; V = I R *<) V = E I r ;) E = I R8 9 = Ix2 I = 4.5 A Vab = I Rab = 4.5x1 Vab = 4.5 V Ans

16.6 &U2 9:>,,-C97:= *:886=:F <=F86=:F*<):F886=:F+7;>*<; *<*:86=:F (galvanometer) 6<<9: K):C<)>7*8<E <8E87=6:B

R8 E r = 0

I

V

www.schoolDD.com 23

16.6.1 2''2* A9:>68Q)*+,,- =::8>C;=:>)*+,,- >*<*<*:86=:F A*:886=:F ??=>=>=F (shunt) K88=Rs 8=: >C*<*:86=:F 9:*C)*+=:> I A+:+ 9:+D*<:86=:F>C IG +<9:D>=F>C IS ;B*<*:86=:F *<)>=F=:> >>78=>F)<:>=F ;)>C8=>F)>7:*<*:86=:F VS = VG ISRS = IGRG

;) RS = H(H

I

*<) I = IG + IS 16

G=:?*<*:86=:F88= 1000 :F8 *<))*+,,-+B+ 50 8*:8*F8+A*:886=:F 9:>)*+,,-+B+ 100 86<<6*:8*F . ;)=:>=F88 . 8=:*:886=:FA

;,,-C97:=

E , r

R

I

*:886=:F

E , r

R

I

A

IG = 50JA RG = 1000 Ω

RS = ?

I = 100 mA G

IS

=:*:886=:F*CC:8>C;,,- 9:>)*+ I

>=F

RG IG

RS

I G

*:886=:F A

IS

G

www.schoolDD.com 24

. RS = ? ;B I = IG + IS IS = I - IG IS = 100x10

-3 50x10-6 A *<) VS = VG (=:>) ISRS = IGRG

RS = H(H

I

= '

.D' =

.D

RS = 0.5 Ω Ans . RA = ?

;B (K =

(H +

(I (=:>)

(K =

+

. =

1

=

.

RA = 0.5 Ω Ans - *:886=:F=:88=:8 89:C>C8=; 9:)*+,,-

;<:+

16.6.2 "*'2* A9:>8=>F ,,- ;,,-=:>C;=:> 8=>F,,-

>*<*<*:86=:F A<=F86=:F? ?=>=8><=6 <::F (multiplier) 88= Rm 8=::8>C*<*:86=:F 9:*C8=>F)<:8><=6 <::F Vm :+A8=>F+B+)>7:*<*:86=:F VG

=:<=F86=:F *CC>C=>= R 9:>8=>F,,-<>7+::=>=

;,,-C97:=

b a

E , r

R

I

b a

<=F86=:F

E , r

R

I

V

V

G

www.schoolDD.com 25

V = Vm + VG

V = IGRm + IGRG V = IG(Rm + RG)

Rm =

H - RG

;B*<*:86=:F *<)8><=6 <::F=::8> >>78=>F=:> ;)>C8=>F)<:8><=6 <::F C>C8=>F)>7:*<*:86=:F 17

G?*<*:86=:F=>: 16 8+A<=F86=:F 9:>8=>F+B+ 10 <=F . ;)=:8><=6 <::F 88= . :=:8><=6 <::F *<*:86=:F +8G>8=>F+B+ . 8=:<=F86=:F8 . Rm = ? ;B V = Vm + VG V = IGRm + IGRG 10 = 50x10-6xRm + 50x10

-6x1000

Rm = D.

'

Rm = 200,000 Ω Ans

8><=6 <::F

RG IG Rm

VG

G

Vm

<=F86=:F V

RG = 1000 Ω IG = 50 JA Rm = ?

VG

G

Vm

V

www.schoolDD.com 26

. G Rm = 0 , VG = ? ;B VG = IGRG = 50x10-6x1000 VG = 50x10

-3 V Ans . RV = ? ;B RV = Rm + RG (=::8) = 200.000 + 1000 RV = 201,000 Ω Ans

- <=F86=:F=:88=+B8 89:C>C8=; 9:)*+,,-

;<:+

16.6.3 "2*''2* A9:>8= ?>>*=)<:=>=>7

:F886=:F):C*<*:86=:F =::8>C=>=* R0 *<)*C==: E 89:=:>8= RxI ?>> x *<) y *=)<:=>= ?C; *<)8)*+,,-D:F886=:F 8D<?E8::F886=:F CK:A8= ;BA;,,-*CC:8 ;) E = Vr + VRX + VRG + VR0 E = I r + I RX + I RG + I R0

y x

:F886=:F

R O R

=>=

y x

R0

RX

RG E , r

I

G

:F886=:F O

?>> x *<)y *=)<=>= 9:>8=

G

www.schoolDD.com 27

>7<9:

N S

E = I (r + RX + RG + R0)

I = 0

-21 (L1 (H1 (M/

- 89:?>> x *<) y *=)> Q)78= Rx = 0 )*+,,-;)88+ E8;)C8

+ (=E8+<)9:7 0 :F8 :F886=:F>8==:?>> x *<) y 9:=;+:CE87 0 :F89:8 GE887 0 :F8 =:>C8=: R0 ;)>E87 0 :F8 :?>8=

16.7 &' '()* ''_

16.7.1'_ ''_

'_ (Magnet) 8G >=G+8GB<E 8>7*8<Eo8=6*<)*8<E+7:K8B=I> **8<E **8<E8+8C>=6>7 1. >7*8<E (magnetic pole) >7*8<E:BC6Q<>7+::**8<E 8:?;*8<E*8+8GBD=)C

<E8C6Q:9 2. 6:>7*8<E =6*8<E;)8 2 >7 9:>79: (north pole)*<)>7= (south pole) >79::**8<E;)

769: +>7=;)76=+8: 3. *)?)>7*8<E8 2 *CC - *B> 6;?>7*8<E=6>8<> - *D<>>6;?>7*8<E6>8<> 6:**8<E

S N N S

N S S N

S N S N

C 1]'U2G J E

www.schoolDD.com 28

''_ (magnetic field) +8*8<E 8G C6Q*8<E+*)?G *<)+**)? :>9:8;+8*8<E ++8*8<E

- ++8*8<E @:**8<E;)86;>79:>>7= - ++8*8<E @**8<E;)86;>7=>>79:

''_" ?8E86KA*8<E<E G=>:B*9:==<:<8;):BC< A7*+ <) =6=> +89:>C8**8<E:B;<< **8<E< >79::**8<E<:B<>7<=@B86+=F *<)>7=:**8<E< :B<>7<9:@B86+=F

N N

S

N

>7<=

>7<9:

S

N

++8*8<E ;+)6 x 88++8*8<ED A=?*+8*8<EABF

++8*8<E<

www.schoolDD.com 29

d*'_ ,<>KF*8<E WNX 8G ;?+**8<E)<D 97D6*=>7H>C 97D6>7 8AC:F (Wb) 8*,<>KF*8<E 9::+8*8<E W BX 8G ,<>KF*8<E=: 97*=>7H 8AC:F =:=8= 9: +< (T) 18

89:,<>KF*8<E 5 x 10- 4 C:F D 97 10 =K=68= K=>7H>C,<>KF*8<E ;8*,<>KF*8<E

2 2HB&'=TH ''_ 89::@8);,,- <9:C6Q8+8*8<E ;)8*9:;+8*8<E)?=::@7 **8<EK;)?6<9:::@<;68

B = O

Φ = 5x10-4 Wb

A = 10x10-4 m2

97 A (m2)

S N

,<>KF*8<E N (Wb)

; B = Q

= =

=

B = 0.5 T Ans

F v +q

*+8*8<E86=>7H)

F v

+q

*+8*8<E86=>7H::;)

www.schoolDD.com 30

:**8<E;8+>8 >oF F = **8<E)?=:); q (N) q = );,,-C:@<9:D+8*8<E (C) V = 8E::@ (m/s) B = +8*8<E (T) 6:**8<E (F) n89: 89:>67>7+6:8E (v) 67>7++8*8<E (B)67>*889: ;)76:* (F) )?=::@8);C (+q) Q :@8);<C (-q) :6<=: 6:* (F) ;)=8>C67:67>*889: 19

:6<=:8); -1.6x 10 -19 B<:8CF<9:8E=> 1.0x 10 7 8==:6 6;K +8*8<E+8?+8: 5.0 x10 -3 +< *<)+886=>7H ) ;*<)6:**8<E)?=::6<=:

F = qvB

F

B v

+q 90° F

B v

-q 90°

F

B v

v -q

:@8);,,-C :@8);,,-<C

; F = qvB = F = 86 Ans

www.schoolDD.com 31

2' G 2.J ''_ 89:<=>?8)*+,,-D Q):B+8*8<E;)8*9:;+8*8<E)?=:<=>? >77 ))*+,,-<=>? 6;<9:::6<=::6+)8E<:<9: >>789:<=>?=>7H >C+8*8<E ;)6*)?=::6<=::6+)<7 =8+8 F = qvB 9:;:6<=::6+) :B@<=>? >7*67 ;?<=>?<9:6:*>7 :*)?=:<=>? ;8+>8 >oF ; F = qvB ---1 ;68:)*+,,- I = R

>>7 q = It

*<)8E v = S = ℓ

* q *<) v 1

;) F = It(ℓ) B

F = *)?=:<=>? (N) I = )*+,,-D<=>? (A) ℓ = 8<=>? (m) B = +8*8<E (T) 6:*)?>C<=>? (F) n89: >CQ*)?=:@8); 9:;<9:::6<=:K8);<C ;)86=8>C6:)*+,,- >>7G?89:67>7+76:)*+,,- (+89:6:); +) 67>*889:;)76:*>B

B

I

N

S

ℓ F

B I

N

S

*)?=:<=>?8)*+,,-D Q):B+8*8<E

F = IB

www.schoolDD.com 32

20

<=>? 20 K=68= 8< 50 >8=>7H>C+8*8<E+8?+8: 2 +< G8)*+,,- 10 *:8*FD< *<8D<< <9:*C ;8:<=>?(86*8G:<) 16.7.2 3 ''_

. ''_12 89:)*+,,-D<=>?= ;)6+8*8<E:C=>?6:+8*8<E; n89:?89::C<=>?= 67>*889: 76:)*+,,- 6:67>7+ 9:6:+8*8<E

I

B

I

B

F

B I

90°

F

B I

ℓ = 0.2

F

B = 2 T I = 10 A

N

S

; F = IℓB = 10x0.2x2 F = 4 N 8;n: 2 :6=> ∑F = ma 4 = 50x10-3xa

a = &

.

a = 80 m/s2 Ans

n89: 6:+8*8<E:<=>?=

www.schoolDD.com 33

1. ''_12"d2.* <K<:F A<AB<+6 89:D)*+,,- D<K<:F ;)8+8*8<E67 K6;n89: G+*<E::*<:K<:F 89:)*+,,-DK<:F *<E::;)8+8C>=6A*8<E,,- *=89:88)*+,,-*<E::;)8+@ *8<E>

I

B

I

I

B I

+8*8<E:<=>?B=I=8n89:

*<E:: I

B

B

N S

I

K<:

www.schoolDD.com 34

16.7.3 2 31' G 89:?<=>?+= 2 + 8> *<D)*+,,-<>7+: ;)6*)?=:+<>7+: 9:;+8*8<E67;)*+,,-D<=>? *=<)+

89:)*+,,-D<=>?>7+:+ 6;Q<=>?+1 ;)8+8*8<E B1 67:C< >>7<=>?+ 2 ;):B+8*8<E B1 6* F 12 )?=:<=>?+ 2 Q)>89: 6;Q<=>? 2 ;)8+8*8<E B2 67:C< *<)<=>?+1 ;):B+8*8<E B2 6* F 21 )?=:<=>?+ 1 ;)+>=G)*+,,-D<=>?6> *)<>7+:;)A*B *<)G6:)*+,,- +>;)A*D<>> >B

16.7.4 21' G 2.J ''_ 89:?<=>?B+<8 +8*8<E *<D)*+,,-<=>? ;)6*)?>C<>B

I1

B2

F

F21 F12 B1

I2

I1

B2

F

B1

I2

I1

B2

F

B1

I2

I1

B2

F

F21

B1

I2

F12

. )*+ I 6>

. )*+ I 6+>

www.schoolDD.com 35

;B* F ;+8 F = IℓB = IbB 9:;*>7+:8> *=6=8> *<)> ;A*BC ?< 68:C *BF<)<+: G? 8< PS *<) QR = a 8< PQ *<) SR = b 89:8:B=>:<;) ;68:88=FBC = *x ))=>7H)**>7+: M = F (a cosθ) = IbB (a cosθ) M = IAB cosθ (89: A = axb = 97:<) G<8< >;? N :C;) M = NIAB cosθ ;+8;)E Mmax 89: cosθ = 1 9: θ = 0° *<) Mmin 89: cosθ = 0 9: θ = 90°

21

<=>?B+<8D9D 8;? 1000 :C 88 5 K=68= *<) 8 K=68= :B+8*8<E+8?+8: 1 +< G8)*+,,- 2 *:8*F D< ;88=F:*BC 67 89:)C:<?88 60 >C+8*8<E

b

a

S

R Q

P

I

I

I B B F

F

a cos θ F

F

a S

θ P B

www.schoolDD.com 36

16.8 '22*

8:=:F,,-A9:89:< <>,,-A <>< :><>:688=F:*BC8<89:D)*+,,-<=>7H>C+8*8<E ?8:=:F,,-8:C*8 ;B . )*+,,-<D=8*)C PQRS ?688=F:*BC8<E86 89:<8;)C:<=>7H>C+8*8<E 8H9:;)?<8=::<E: 8D<?* a *<) b <=?*; x *< y +>8D>+>C:886==:F y *<) x =8<?>C ?)*+,,-<86=8* SRQP *<)88=F:*BC67=:7;)?<8668=: >B . - 88=F:*BC;)88+89:)C:<>C+8*8<E *<)8:

+ (M=0) 89:)C:<=>7H>C+8*8<E (=8+8 M = F (a cosθ))

a cos 60 F

F a = 0.05

60° B = 1 T

y x b a

P

Q R

S

I

I

I B B F

F

N S

88=F:*BC M = F (a cos60) = IℓB (a cos60) = 2x0.08x1.0x (0.05x0.5) = 4x10-3 N ;?< N = 1000 :C M>78 = NM = 1000x4x10

-3 M>78 = 4.0 N-m Ans

+):C:8:=:F,,-)*+=

y x b a

*8

*

:886==:F

S

R Q

P

I

I

I B B F

F

N S

B . B .