1. SchoolDD.com
16
www.schoolDD.com

2. 16
16.1
(electric current)
. .
F
. F F
F F F F
F F F F
.
F F F
F F F F F
F F F F F F F F F F F
F F F F F F F
F F F F F F F
16.1.1
F
(free electron) FF
F F F F F F (Brownian motion)
F F
F F www.schoolDD.com 1

3. F F F F F
F F F
(drift velocity) F F
VA VB VA VB
VA = VB VB > VA
F F
F F F F F F
F F F (VA = VB) (VB > VA) F
16.1.2
F F
F F F
F F F F F F (A)
I=
I= (A)
Q= ( ) F (C)
t= F (s)
I E
F 1
F 1.25 F F F F F F
F 5 F F
F F www.schoolDD.com 2

4. I = 1.25 A t=5,Q=?
I=
Q = It
= 1.25x5.0
Q = 6.25 C Ans
F 2
F F F F F F 3.2 F
F F 5.0 ( 1.6 X10-19 )
F
I = 3.2 A
I=
Q = It
I I
Q = 3.2x5.0 C
F 1 1.6 X10-19 C
=
= 1x1020 Ans
F F
I , F E
E
(I)
F
s = vt
F F www.schoolDD.com 3

5. I= Q = Ne = (nAs)e = (nAvt)e = nevtA
I = .
I = nevA
n= F ( / m3)
e= (1.6 x 10- 19 C)
v= (m/s)
A= (m2)
F 3
F 5.0 x 1028 F F F 2.5 F
F F 0.30 F F
F
A = 2.5x10-6 m2
I=? I = nevA
= 5x1028x1.6x10-19x0.3x10-3x2.5x10-6
n = 5x1028 I = 6.0 A Ans
v = 0.3x10-3 m/s
16.2 F F (I) F F (V)
16.2.1 F F
F F F F F
I V
I = KV ( K= F )
=
=R ( = R)
V=IR F
R= F F F F F F ( )
F F www.schoolDD.com 4

6. - F F F F
I I I I
V V V V
F
F 4
F F F F F F
V (V)
3
2
1
I (A)
0 0.2 0.4 0.6
F 5
F F F 1.0 F F F F 1.0 F F
F F
R = 1x106
F V = IR
I = 1x10-3 A I
= 1x10-3x1x106
V = 1x103 V Ans
V=?
F (Resistor)
F F F F F F F F
F 2
1. F (Fixed resistor) F F F
F F F F F F
F F www.schoolDD.com 5

7. 1 2 3 4
4 F
F
1
0 0 1 -
2
1 1 101 1%
3
2 2 102 2%
F 3 3 103 -
4 F
4 4 104 -
F F
5 5 105 - 3
F 15x10 F
6 6 106 -
2% F 15,000 F
F 7 7 - -
300 F F F 14,700 F
8 8 - -
15,300 F
9 9 - -
- - 10-1 5%
- - 10-2 10 %
2. F F (Variable resistor) F F F F F
F F F F F
F F 1 3 F F 2 F F
F F
1 3 F F F 2
A
2 F 1 F 3 F
F F
(Diode)
F F F F F
F 2
I A F F A F
F F F
F F www.schoolDD.com 6

8. - F F F F
F 6
F a F F b F F C
F F F F
F
F a F = 30x102 150
3 0 102 5%
F
F b F = 18x103 1800
3
1 8 10 10%
F c F =
16.2.2 F
F F F
F F F F F F
F F
F F F F (V) (I) F
(R) F F
. F
R
R= F F
F F = 1.6x10-8 m , = 1.7x10-8 m
F = 1010- 1014 m , = 1014- 1018 m
F 7
F 10 F F F F 1 F
F F F 2 F F F F F
F ( = 1.7x10-8 m)
F F www.schoolDD.com 7

9. d = 1x10-3 m
F = 10 m
F A= = = 7.85x10-7 m2
R=
R1 =
R1 = 0.216 Ans
d = 2x10-3 m
F = 10 m
A= = = 3.14x10-6 m2
F
R=
R2 =
R2 = 0.054 Ans
= =4
1 F F 2 F 4 F Ans
G F F F ( F )-1 F (S)
G=
F F F
( F )-1 F F (S/m)
=
16.2.3 F F
F F F
T ---> R
F F F F F
T ---> R
F F
T ---> R
F F www.schoolDD.com 8

10. (Superconductivity) F F ( = 0) F
F (critical temperature) F (Supper
conductor)
16.3
16.3.1 ( E) F F (V)
F F ( F F ) F F F F
F F F
F F
F R
I
I I
E I
F
F F F R F
E F r F F I F F
R
VR
I
V
r E
Vr
F ( ) F F F Q
E F F F r R F F Q F F
F F
F WE = F
WR = F F R
Wr = F F r
F FF WE = W R + W r
QE = QVR + QVr
F E = VR + Vr
F F www.schoolDD.com 9

11. E = IR + Ir
F I=
F V F F F F V = VR
F V F F R F F FV E F F V=E
F 8
F 12.0 F F 2.0 F F F 7.0
F F F F F F F F F F F
F F F F F F
R = 20
VR
I
V=?
r = 2 E = 12 V
Vr
I E = VR + Vr
E = IR + Ir
I= = = A
V = VR = IR
= x70
V = 11.67 V Ans
F F F F
V=?
F V E = 12 V Ans
r = 2 E = 12 V
F F www.schoolDD.com 10

12. 16.3.2
R
I V I
E
FQ= F F t (C)
I= F F (A)
V= F F F (V)
W= F F ( J)
W = QV
I= Q = It V = IR
W = ItV = I2Rt =
P F F F F F (W)
P= P= = = IV
F 9
F 1.5 F2 F F F 20 F
F 20 F F 15 F F 1 F
t = 20 hr
I=20 mA
E = 1.5x2 = 3 V
F W = QV
= ItV
F F www.schoolDD.com 11

13. = 20x10-3x(20x60x60)x3
W = 4320 J
F F 1 F = = 0.007 / Ans
16.4 F F
16.4.1 F F
1. F
F F F F F
V1 V2 V3
R1 R2 R3
I1 I2 I3
V
I
E
F FF
- F F F
I = I1 = I2 = I3
- F F = F F F
V = V1 + V2 + V3
V = V1 + V2 + V3
V = IR ( F )
IR = I1 R1 + I2 R2 + I3R3
R = R1 + R2 + R3 (I = I1 = I2 = I3)
R = F R1,R2 R3
2. F
F F F F
F F www.schoolDD.com 12

14. V1 = V2 = V3
R1
I1 R2
I2
I3 R3
I I
V
E
F FF
- F F F F F = F F
V = V1 = V2 = V3
- F = F F F
I = I1 + I2 + I3
I = I1 + I2 + I3
V = IR I=
= + +
= + + (V = V1 = V2 = V3)
R = F R1 , R 2 R3
- F F F F F F F
F F F F F F F
- F F F F F
F 10
F F F
. FS . FS
F F www.schoolDD.com 13

15. 1 2
A B
S
I
3 4
. FS 1 2
F F R1 R2
A B
R3 R4
I
3 4
F R1 R2 F
F F R 12 = R 1 + R 2 = 1 +2 = 3
F R3 R4 F
F F R 34 = R 3 + R 4 = 3 +4 = 7
F F
3
R12
A B
R34
I
7
F R 12 R 34 F
F F = + = + =
=
R = 2.1 Ans
. FS
F F
1 2
R1 R2
A B
R3 R4
I
3 4
F R1 R3 F
F F www.schoolDD.com 14

16. F F = + = + =
=
R13 =
F R2 R4 F
F F = + = + =
=
R24 =
F F
A 3/4 4/3 B
R13 R24
I
F R 13 R 24 F
F F R = R13 + R24
= + =
=
R = 2.08 Ans
16.4.2 F
1. F
F F F F F
R
I
r1 E1 r2 E2 r3 E3
F FF
- = F
E = E1 + E2 + E3
F F F F
F F www.schoolDD.com 15

17. r = r1 + r2 + r3
2. F
F F F F
R
I r1 E1
r2 E2
r3 E3
F F F F E1 = E2 = E3
F FF
- = F F F
E = E1 = E2 = E3
- F F F F
= + +
- F F F F
F
F 11
F F 0.25 F F F 8 F
F F 0.16 F F
F F F F F E r
F F www.schoolDD.com 16

18. F
R=8
I = 0.25 A V
r1 E1 r2 E2
E = E1 + E2 = E + E = 2E
F r = r1 + r2 = r + r = 2r
F F
R=8
I = 0.25 A
V
r E
V = E Ir
V = IR
F IR = 2E I(2r)
0.25x8 = 2E 0.25(2r)
E 0.25r = 1 ---1
F
R=8
V
I = 0.16 A r1 E1
r2 E2
E = E1 = E2 = E
F = + = + =
r =
F F
R=8
I = 0.16 A
V
r E
F F www.schoolDD.com 17

19. V = E Ir
V = IR
F IR = E I( )
0.16x8 = E 0.16( )
E 0.08r = 1.28 ---2
2-1, -0.08r + 0.25r = 0.28
0.17r = 0.28
r = 1.7 Ans
F r 2 F E 0.08(1.7) = 1.28
E = 1.41 V Ans
16.5 F F
F F F F F
F F
F 12
F F a,b c
F E1 = 6 V , E2 = 6 V , r1 = 1 , r2 = 1 , Ra = 7 , Rb = 4 , Rc = 12
b
a
c
I
r1 E1 r2 E2
F
F b c F F F F a
F b c = + = +
= = =
Rbc = 3
F a bc R = Ra + Rbc
= 7+3
R = 10
E1 E2 F
E = E1 + E2 = 6 + 6 = 12 V
F F www.schoolDD.com 18

20. F r = r1 + r2 = 1 + 1 = 2
F F
R
I
V
r E
V = E Ir
V = IR
F IR = E I r
Ix10 = 12 Ix2
I = 1.0 A
F F a , Ia = I = 1.0 A Ans
F 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
F 13
F F 10 F F F F
F F 1.2 F F F 6 F F F F
F F F F F F F
F F F 6 V.
F F F F F 1.2 V. F F 10
mA.
F F www.schoolDD.com 19

21. F F F F F F F F F
F R F
VR VD
R
I F
V
E,r=0
V = VR + VD
0
V = E Ir = E
F E = VR + VD
VR = E VD = 6 1.2
VR = 4.8 V
F
VR = I R
R= =
R = 480 Ans
F 14
2 F F F F F F
. F
. F F F F
. F
. F 10
. F
R = 0.5
I=2A
r=0 R1
E=6V
.
F F F F F
I = I = 2 A Ans
F F www.schoolDD.com 20

22. . VR = ?
F V = IR
VR = 2x0.5
VR = 1.0 V Ans
. R1 = ?
E = I r + I R + I R1
6 = 2x0 + 2x0.5 + 2xR1
R1 =
R1 = 2.5 Ans
. W=? t = 10 s
W = QV
= QE
= ItE (I = )
= 2x10x6
W = 120 J Ans
. PR = ?
W = QV
P=
P=
PR = =
= I2R = 22x0.5
PR = 2 W Ans
F 15
F F F a b
I I
R1 = 1 R1 = 1
a a
E=9V E=9V
R2 = 2 R2 = 2 R3 = 2
b
b
. .
F F www.schoolDD.com 21

23. . V2 = ? I
V2 V2 = I R2
F R2 I
E V R
R1 R2 F r=0
R = R1 + R2 = 1 + 2 = 3
V = IR
0
V = E Ir
F E = IR
9 = Ix3
I =3A
V2 = I R2 = 3x2
V2 = 6 V Ans
. V2 = ?
R2 R3 F
F = + = +
Rab = 1
R1 Rab F
F R = R1 + Rab = 1 + 1 = 2
V = IR 0
V = E Ir
F E = IR
9 = Ix2
I = 4.5 A
Vab = I Rab = 4.5x1
Vab = 4.5 V Ans
16.6
F F F F F F F F
F (galvanometer) F F F
F
F F www.schoolDD.com 22

24. 16.6.1 F
F F F
R R
F A
I I
E,r E,r
F F F F
F I
F F F F F F (shunt) F
Rs F F G F F I F F F
F F IG F F F F IS
I IG RG
G
IS
RS
F
F A
F FF F F F F F F
F F F
VS = VG
ISRS = IGRG
F RS =
I = IG + IS
F 16
F F F F 1000 F 50 F
F F F 100 F
. F F F F
IG = 50 A RG = 1000
. F F F I = 100 mA
G
IS
RS = ?
F F www.schoolDD.com 23

25. . RS = ?
I = IG + IS
IS = I - IG
IS = 100x10-3 50x10-6 A
VS = VG (F )
ISRS = IGRG
RS =
= =
RS = 0.5 Ans
. RA = ?
= + ( F )
= + = =
RA = 0.5 Ans
- F F F F F F
F
16.6.2 F F
F F F F F F
F F
V
R a R
a b
b
I
I
E,r E,r
F F F F V F R
F F F
F F F F F F F
(multiplier) F Rm F F G F F F F
F Vm F F F F F VG
F F www.schoolDD.com 24

26. IG Rm RG
G
F
Vm VG
F F V
V = Vm + VG
V = IGRm + IGRG
V = IG(Rm + RG)
Rm = - RG
F FF F F F F F
F F F F F F F
F 17
F F F 16 F F F F F F 10 F
. F F F F F
. F F F F F F F F
. F F F F F
IG = 50 A Rm = ? RG = 1000
G
Vm VG
V
. Rm = ?
V = Vm + VG
V = IGRm + IGRG
10 = 50x10-6xRm + 50x10-6x1000
Rm =
Rm = 200,000 Ans
F F www.schoolDD.com 25

27. . F Rm = 0 , VG = ?
VG = IGRG
= 50x10-6x1000
VG = 50x10-3 V Ans
. RV = ?
RV = Rm + RG ( F )
= 200.000 + 1000
RV = 201,000 Ans
- F F F F F F
F
16.6.3 F F
F F
F F
R O
x R y
F
x y
F F F
F F F F G F F F R0 E
F F Rx F x y F F
F F F F F F F F F F
RG
E,r G
R0
I
x y
RX
F F O
FF
E = Vr + VRX + VRG + VR0
E = I r + I R X + I RG + I R0
F F www.schoolDD.com 26

28. E = I (r + RX + RG + R0)
I=
- x y F Rx = 0 F
( ) 0 F F F F F F x y
F 0 F F F F 0 F F F R0
0 F F F
16.7 F F F
16.7.1 F F
F (Magnet) F F F F
F F F F F
F F
1. F (magnetic pole)
F F F F F
F F
2. F
F 2 (north pole) F (south pole) F F
F F F
N
S
3. F F 2
- F F F
- F F
S N N S
F
N S S N
S N S N
F
F F www.schoolDD.com 27

29. F (magnetic field)
F F F F
F F F F
- F F F F F
- F F F F F
S
N N
N
x F F F F
F F
F F F
F
F F F FF F
F F F F F F F F F
F F F F F F F F F F F
F
S
N
F
F F
F F www.schoolDD.com 28

30. F F
F F F F F
F F (Wb)
F F F F B F F F F
F F F (T)
A (m2)
S N B=
F F (Wb)
F 18
F F 5 x 10- 4 F F F 10 F F
F F F
A = 10x10-4 m2
B=
=
B = 0.5 T Ans
= 5x10-4 Wb
F F
F F F
F F F F
v
+q F
+q v F
F F F
F F www.schoolDD.com 29

31. F F F
F = qvB
F= F F q (N)
q= F F (C)
V= (m/s)
B= F (T)
F (F) F F F (v)
F (B) F (F) F (+q)
(-q) F (F) F F
F
F
-q
+q 90° B
v
90° B
v F
v B
F 19
-1.6x 10 -19 F F 1.0x 10 7 F F
F F 5.0 x10 -3 F
F F
F = qvB
-q v =
F = Ans
F F www.schoolDD.com 30

32. F F F F
F F F F F
F
F F F F=
qvB F F
N N I
F
I B B
S S
F F F F
F F F
F = qvB ---1
I= q = It
v= =
F q v 1
F F = It( ) B
F=I B
F= F (N)
I= F (A)
= (m)
B= F (T)
(F) F F F F
F F
F ( +) F
F F www.schoolDD.com 31

33. F
F
90° B
I
I B
F 20
20 50 F 2 F 10
FF F F F ( F F F
)
F=IB
= 10x0.2x2
= 0.2
N F=4N
F
F F 2
B=2T
= ma
I = 10 A 4 = 50x10-3xa
S
a=
a = 80 m/s2 Ans
16.7.2 F F
. F
F F F F F
F F
F
I I
B
B
F F
F F www.schoolDD.com 32

34. I
I
B
B
I
I
F F F
. F F
F F F F F F
F F F F F F F F
F F F F F F F F F
F
B
N S
B
I I
F F
F F www.schoolDD.com 33

35. 16.7.3 F F F
F 2 F F F F
F F F F F F
B2 B1 B2 B1
F21 F12
F21 F12
F F
I1 I2 I1 I2
B2 B1 B2 B1
F F
I1 I2 I1 I2
. I . I
F F F F 1 F B1
F 2 F F B1 F 12 F F 2
2 F B2 F 1 F
F B2 F 21 F F 1
F F F F F
F
16.7.4 F F F F
F F F F
F F www.schoolDD.com 34

36. Q a R
I F
B B
b
F I
P S
I
F F F = I B = IbB F F
F F F F F F
F F PS QR = a
F PQ SR = b
F F F
F
S
a
B
P
F
a cos
FF = x F
M = F (a cos ) = IbB (a cos )
M = IAB cos ( A = axb = )
F N F
M = NIAB cos
F Mmax cos = 1 = 0°
Mmin cos = 0 = 90°
F 21
F 1000 F 5 8 F
F 1 F 2 F F F F
60 F
F F www.schoolDD.com 35