This document discusses electric current and concepts related to electricity. It contains the following key points: 1. Electric current is the flow of electric charge in a conductor. The direction of the flow is from higher electric potential to lower electric potential. 2. The factors that affect the magnitude of electric current include the amount of charge passing through a point in the conductor per unit time, and the resistance of the conductor. 3. Kirchhoff's laws relate the current and potential difference in different parts of an electric circuit.

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

37. F F M = F (a cos60)
F = I B (a cos60)
a = 0.05 = 2x0.08x1.0x (0.05x0.5)
B=1T
60° = 4x10-3 N
F N = 1000
a cos 60 M = NM = 1000x4x10-3
M = 4.0 N-m Ans
16.8 F
Q R R Q
N I F B S N I F
B B B S
F I F I
P S S P
a b a b
x y y x
I I
F
. .
F F
F F
F F F F F F
F
. F PQRS F F F
F F
F F F a b F x y Fy
x F SRQP F F
F F .
- F F F F F F
(M=0) F ( M = F (a cos ))
F F www.schoolDD.com 36