This document discusses electric circuits and concepts related to current, voltage, and resistance. It contains the following key points: 1. It defines basic circuit concepts like current, charge, drift velocity, and explains how current is related to charge, time, and resistance. 2. It provides formulas for calculating current, charge, and resistance and applies them in examples. Current is calculated using charge divided by time. Resistance depends on resistivity, length, and cross-sectional area of a material. 3. It discusses series and parallel circuits, explaining how current and voltage are distributed in each type. In series circuits, current is the same but voltage adds up. In parallel, voltage is the same but current splits

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

3. F ˆ F www.schoolDD.com 2
F F F F ˂ F
˂ F F ˈ F
(drift velocity) F ˂ F ˂
16.1.2 ˂ ˂
˂ ˂ F F
˂
˂ F F ˂ F
F ˈ F F ˈ F F F (A)
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
I =
‫ۿ‬
‫ܜ‬
F
F F
F F F ˂ (VA = VB)
F
F F F F ˂
(VB > VA) ˂ F
˂
VA = VB
VA VB
VB > VA
VA VB

4. F ˆ F www.schoolDD.com 3
F 2
F F F F ˂ F F 3.2 F
F F 5.0 ( ˂ 1.6 X10-19
F)
˂
F F ˂
s = vt
I = 1.25 A
II
I = 3.2 A
t = 5 , Q = ?
˂ I =
୕
୲
Q = It
= 1.25x5.0
‫׵‬ Q = 6.25 C Ans
˂ I =
୕
୲
Q = It
Q = 3.2x5.0 C
F 1 1.6 X10-19
C
‫׵‬ = ଷ.ଶ୶ହ.଴
ଵ.଺௫ଵ଴షభవ
= 1x1020
Ans
I
E
˂ , F E
˂ (I)
F

5. F ˆ F www.schoolDD.com 4
˂ I =
୕
୲
˂ Q = Ne = (nAs)e = (nAvt)e = nevtA
I =
୬ୣ୴୲୅
୲
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
16.2 F F ˂ (I) F F (V)
16.2.1 F F
˂ F F F F ˂ F
I ‫ן‬ V
‫׵‬ I = KV ( K = F )
୚
୍
=
ଵ
୏
୚
୍
= R (
ଵ
୏
= R)
R = F F ˈ F F F F ( Ω )
V = I R F
A = 2.5x10-6
m2
n = 5x1028
v = 0.3x10-3
m/s
I = ? I = nevA
= 5x1028
x1.6x10-19
x0.3x10-3
x2.5x10-6
‫׵‬ I = 6.0 A Ans
.

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

7. F ˆ F www.schoolDD.com 6
1 2 3 4
F
0 0 1 -
1 1 101
േ 1 %
2 2 102
േ 2 %
F 3 3 103
-
4 4 104
-
5 5 105
-
6 6 106
-
F 7 7 - -
8 8 - -
9 9 - -
- - 10-1
േ 5 %
- - 10-2
േ 10 %
2. F F (Variable resistor) ˈ F F F F F
˂ F F F F F
F F 1 3 F F 2 F F ˂
(Diode)
ˈ F F F F F
˂ ˂ ˂
F ˂ 2
F
2
F F
31
A
FI A FF A
F F 2
F 1 F 3 F
F F
F ˂ F F ˂
4 F
1
2
3
4 ˈ F
F F
F 15x103
F
േ2 % F 15,000 F േ
300 F F F 14,700 F
15,300 F

8. F ˆ F www.schoolDD.com 7
- F ˂ F F F ˂ ˈ ˂
F 6
F a F F b F F C
F F F F
F a F = 30x102
Ω േ 150 Ω
F b F = 18x103
Ω േ 1800 Ω
F c F =
16.2.2 F ˂
F ˂ ߩ ˈ F F
˂ F F F F F F ˂
F ˈ F
F F F F ˂ (V) ˂ (I) F
(R) F F
୚
୍
‫ן‬
ℓ
୅
R ‫ן‬
ℓ
୅
F F ߩ = 1.6x10-8
Ω m , ߩ = 1.7x10-8
Ω m
ߩ F = 1010
- 1014
Ω m , ߩ = 1014
- 1018
Ω m
F 7
F 10 F F F F 1 F
F F F 2 F F F ˈ F F
F ( ߩ = 1.7x10-8
Ω m)
1 8 103
േ 10%
3 0 102
േ 5%
R =
࣋र
‫ۯ‬
F
F
. F
ߩ F F ˂

9. F ˆ F www.schoolDD.com 8
F
F
R =
ఘℓ
୅
R1 =
ଵ.଻୶ଵ଴షఴ୶ଵ଴
଻.଼ହ୶ଵ଴షళ
‫׵‬ R1 = 0.216 Ω Ans
F
F
R =
ఘℓ
୅
R2 =
ଵ.଻୶ଵ଴షఴ୶ଵ଴
ଷ.ଵସ୶ଵ଴షల
‫׵‬ R2 = 0.054 Ω Ans
ୖభ
ୖమ
=
଴.ଶଵ଺
଴.଴ହସ
= 4
‫׵‬ 1 F F 2 F 4 F Ans
˂ G ˈ F F ˂ F ˈ ( F )-1
F (S)
G =
ଵ
ୖ
˂ ߪ ˈ ˈ F F ˂ F ˈ
( F )-1
F F (S/m)
ߪ =
ଵ
ఘ
16.2.3 F F
ˈ F F F
T ---> R
F F F F F
T ---> R
ˈ F F
T ---> R
A =
గௗమ
ସ
=
ଷ.ଵସ୶ሺଵ୶ଵ଴షయሻమ
ସ
= 7.85x10-7
m2
d = 1x10-3
m
ℓ = 10 m
A =
గௗమ
ସ
=
ଷ.ଵସ୶ሺଶ୶ଵ଴షయሻమ
ସ
= 3.14x10-6
m2
d = 2x10-3
m
ℓ = 10 m

10. F ˆ F www.schoolDD.com 9
(Superconductivity) F ˂ ˈ F (ߩ = 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 F F R F ˂
E F r F F ˂ I F F
˂ 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 F F WE = WR + Wr
QE = QVR + QVr
F
I
F ˂
E I
F R
I
VR
r E
V
Vr
R
I
E = VR + Vr
I

11. F ˆ F www.schoolDD.com 10
E = IR + Ir
F I =
୉
ሺୖା୰ሻ
F V F F F F V = VR
F V F F R F F F V ؆ 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
I E = VR + Vr
E = IR + Ir
I =
୉
ሺୖା୰ሻ
=
ଵଶ
ሺ଻଴ାଶሻ
=
ଵ
଺
A
V = VR = IR
=
ଵ
଺
x70
‫׵‬ V = 11.67 V Ans
F F F F
F V ؆ E = 12 V Ans
VR
r = 2 E = 12 V
V= ?
Vr
R = 20 Ω
I
r = 2 E = 12 V
V= ?

12. F ˆ F www.schoolDD.com 11
16.3.2 ˂
˂
F Q = ˂ F F t (C)
I = ˂ F F (A)
V = F F F (V)
W = ˂ F F ( J)
I =
୕
୲
Q = It V = IR
‫׵‬ W = ItV = I2
Rt =
୚మ୲
ୖ
˂ P ˂ F F F ˈ F F (W)
F 9
F 1.5 F 2 F F F ˂ 20 F
F 20 F F 15 F ˂ F ˂ 1 F
˂ F W = QV
= ItV
E
I
R
I V
W = QV
P =
‫܅‬
‫ܜ‬
P =
୛
୲
=
ItV
୲
= IV
E = 1.5x2 = 3 V
t = 20 hr
I=20 mA

13. F ˆ F www.schoolDD.com 12
= 20x10-3
x(20x60x60)x3
‫׵‬ W = 4320 J
F ˂ F ˂ 1 F =
ଵହ୶ଶ
ସଷଶ଴
= 0.007 / Ans
16.4 F F
16.4.1 F F
1. F
ˈ F F F F F
F F F
- ˂ 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 = F R 1 , R 2 R 3
2. F
ˈ F F F ˈ F
R3R1 R2
I1
E
I
V
V1
I2 I3
V2 V3
R = R1 + R2 + R3
(I = I1 = I2 = I3)

14. F ˆ F www.schoolDD.com 13
F F F
- 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 =
୚
ୖ
୚
ୖ
=
୚భ
ୖభ
+
୚మ
ୖమ
+
୚య
ୖయ
R = F R1 , R2 R3
- F F F F F F F
˂ F F F F F ˂ F F
- F F ˈ F F F
F 10
F F F
. F S ʽ . F S ʽ
E
V1 = V2 = V3
R3
I I
I1
V
I3
R2
I2
R1
૚
‫܀‬
=
૚
‫܀‬૚
+
૚
‫܀‬૛
+
૚
‫܀‬૜
(V = V1 = V2 = V3)

15. F ˆ F www.schoolDD.com 14
. F S ʽ
F F
F R 1 R 2 F
F F R 12 = R 1 + R 2 = 1 +2 = 3 Ω
F R 3 R 4 F
F F R 34 = R 3 + R 4 = 3 +4 = 7 Ω
F F
F R 12 R 34 F
F F
ଵ
ୖ
=
ଵ
ୖభమ
+
ଵ
ୖయర
=
ଵ
ଷ
+
ଵ
଻
=
଻ାଷ
ଶଵ
ଵ
ୖ
=
ଵ଴
ଶଵ
‫׵‬ R = 2.1 Ω Ans
. F S ʽ
F F
F R 1 R 3 F
4 Ω3 Ω
2 Ω
B
S
1 Ω
I
A
R4R3
R2R1
4 Ω3 Ω
2 Ω
B
1 Ω
I
A
R34
R12
7 Ω
B
3 Ω
I
A
R4R3
R2R1
4 Ω3 Ω
2 Ω
B
1 Ω
I
A

16. F ˆ F www.schoolDD.com 15
F F
ଵ
ୖభయ
=
ଵ
ୖభ
+
ଵ
ୖయ
=
ଵ
ଵ
+
ଵ
ଷ
=
ଷାଵ
ଷ
ଵ
ୖభయ
=
ସ
ଷ
‫׵‬ R13 =
ଷ
ସ
Ω
F R 2 R 4 F
F F
ଵ
ୖమర
=
ଵ
ୖమ
+
ଵ
ୖర
=
ଵ
ଶ
+
ଵ
ସ
=
ଶାଵ
ସ
ଵ
ୖమర
=
ଷ
ସ
‫׵‬ R24 =
ସ
ଷ
Ω
F F
F R 13 R24 F
F F R = R13 + R24
=
ଷ
ସ
+
ସ
ଷ
=
ଽ ାଵ଺
ଵଶ
=
ଶହ
ଵଶ
‫׵‬ R = 2.08 Ω Ans
16.4.2 F
1. F
ˈ F F F F F
F F F
- ˂ = ˂ F
F F F F
R24R13
4/3 Ω B3/4 Ω
I
A
E3r1 E1
R
I
r2 E2
r3
E = E1 + E2 + E3

17. F ˆ F www.schoolDD.com 16
2. F
ˈ F F F F
F ˂ F F F E1 = E2 = E3
F F F
- ˂ = ˂ F F F
- 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
r = r1 + r2 + r3
E = E1 = E2 = E3
૚
‫ܚ‬
=
૚
‫ܚ‬૚
+
૚
‫ܚ‬૛
+
૚
‫ܚ‬૜
E3
r2 E2
R
I r1 E1
r3

18. F ˆ F www.schoolDD.com 17
F
˂ E = E1 + E2 = E + E = 2E
F r = r1 + r2 = r + r = 2r
F F
V = E I r
V = IR
F IR = 2E I(2r)
0.25x8 = 2E 0.25(2r)
E 0.25r = 1 ---1
F
˂ E = E1 = E2 = E
F
ଵ
୰
=
ଵ
୰భ
+
ଵ
୰మ
=
ଵ
୰
+
ଵ
୰
=
ଶ
୰
r =
୰
ଶ
F F
r1 E1
R = 8 Ω
I = 0.25 A
r2 E2
V
V
r E
R = 8 Ω
I = 0.25 A
r1 E1
R = 8 Ω
I = 0.16 A
r2 E2
V
V
r E
R = 8 Ω
I = 0.16 A

19. F ˆ F www.schoolDD.com 18
V = E I r
V = IR
F IR = E I(
୰
ଶ
)
0.16x8 = E 0.16(
୰
ଶ
)
E 0.08r = 1.28 ---2
2-1, -0.08r + 0.25r = 0.28
0.17r = 0.28
‫׵‬ r = 1.7 Ω 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 Ω , r2 = 1 Ω , Ra = 7 Ω , Rb = 4 Ω , Rc = 12 Ω
F
F b c F F F F a
F b c
ଵ
ୖౘౙ
=
ଵ
ୖౘ
+
ଵ
ୖౙ
=
ଵ
ସ
+
ଵ
ଵଶ
=
ଷାଵ
ଵଶ
=
ସ
ଵଶ
=
ଵ
ଷ
‫׵‬ Rbc = 3 Ω
F a bc R = Ra + Rbc
= 7 + 3
‫׵‬ R = 10 Ω
E1 E2 F
˂ E = E1 + E2 = 6 + 6 = 12 V
c
r1 E1
a
I
r2 E2
b

20. F ˆ F www.schoolDD.com 19
F r = r1 + r2 = 1 + 1 = 2 Ω
F F
V = E I r
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 =
ଵଶ
ଵ଺
=
ଷ
ସ
= 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.
V
r E
R
I

21. F ˆ F www.schoolDD.com 20
0
F F F F F F F F F
F R F
V = VR + VD
V = E I r = E
F E = VR + VD
VR = E VD = 6 1.2
‫׵‬ VR = 4.8 V
F
VR = I R
R =
୚౎
୍
=
ସ.଼
ଵ଴௫ଵ଴షయ
‫׵‬ R = 480 Ω Ans
F 14
˂ ˂ 2 F F F F F F
. ˂ F
. F F F F
. F
. ˂ F 10
. ˂ F
.
˂ F F ˂ F F F
‫׵‬ I = I = 2 A Ans
VDVR
F
V
E , r = 0
R
I
r = 0
E = 6 V
R = 0.5 Ω
R1
I = 2 A

22. F ˆ F www.schoolDD.com 21
. VR = ?
F V = I R
VR = 2x0.5
‫׵‬ VR = 1.0 V Ans
. R1 = ?
E = I r + I R + I R1
6 = 2x0 + 2x0.5 + 2xR1
R1 =
଺ିଵ
ଶ
‫׵‬ R1 = 2.5 Ω Ans
. W = ? t = 10 s
W = QV
= QE
= ItE (I =
୕
୲
)
= 2x10x6
‫׵‬ W = 120 J Ans
. PR = ?
W = QV
P =
୛
୲
P =
QV
୲
PR =
QVR
୲
=
ItሺIRሻ
୲
= I2
R = 22
x0.5
‫׵‬ PR = 2 W Ans
F 15
F F F a b
R3 = 2 ΩR2 = 2 Ω
b
.
E = 9 V
R1 = 1 Ω
a
I
R2 = 2 Ω
b
.
E = 9 V
R1 = 1 Ω
a
I

23. F ˆ F www.schoolDD.com 22
0
0
. V2 = ?
V2 V2 = I R2
F R2 I
R1 R2 F
R = R1 + R2 = 1 + 2 = 3 Ω
V = I R
V = E I r
F E = I R
9 = Ix3
‫׵‬ I = 3 A
V2 = I R2 = 3x2
‫׵‬ V2 = 6 V Ans
. V2 = ?
R2 R3 F
F
ଵ
ୖ౗ౘ
=
ଵ
ୖమ
+
ଵ
ୖయ
=
ଵ
ଶ
+
ଵ
ଶ
‫׵‬ Rab = 1 Ω
R1 Rab F
F R = R1 + Rab = 1 + 1 = 2 Ω
V = I R
V = E I r
F E = I R
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
RE
r = 0
I
V

24. F ˆ F www.schoolDD.com 23
16.6.1 F
ˈ ˂ F F F ˂
F ˈ F F F F F (shunt) F
Rs F F F F I ˈ F F F
F F IG F F F F IS
F F F 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 ˈ F ˂ F 100 F
. F F F F
. F F ˈ F
˂ F
E , r
R
I
F
E , r
R
I
A
IG = 50ߤA RG = 1000 Ω
RS = ?
I = 100 mA
G
IS
F F F
˂ F I
F
RGIG
RS
I
G
F A
IS
G

25. F ˆ F www.schoolDD.com 24
. RS = ?
I = IG + IS
IS = I - IG
IS = 100x10-3
50x10-6
A
VS = VG ( F )
ISRS = IGRG
RS =
୍ృୖృ
୍౏
=
ହ଴୶ଵ଴షల୶ଵ଴଴଴
ଵ଴଴୶ଵ଴షయିହ଴୶ଵ଴షల
=
ଵ଴଴଴
ଶ୶ଵ଴యିଵ
‫׵‬ RS = 0.5 Ω Ans
. RA = ?
ଵ
ୖఽ
=
ଵ
ୖృ
+
ଵ
ୖ౏
( F )
ଵ
ୖఽ
=
ଵ
ଵ଴଴଴
+
ଵ
଴.ହ
=
ଵାଶ଴଴଴
ଵ଴଴଴
=
ଵ
଴.ହ
‫׵‬ RA = 0.5 Ω Ans
- F F F F F F ˂
F
16.6.2 F F
ˈ F F ˂ ˂ F F F F ˂
F ˈ F F F F F F
(multiplier) F Rm F F F F F F
F Vm F ˈ F F F F VG
F F F F R
F F ˂ F
˂ F
ba
E , r
R
I
ba
F F
E , r
R
I
V
V
G

26. F ˆ F www.schoolDD.com 25
V = Vm + VG
V = IGRm + IGRG
V = IG(Rm + RG)
Rm =
୚
୍ృ
- RG
F F F F F F F F
F F F F F F F
F 17
F F F 16 F ˈ 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
. Rm = ?
V = Vm + VG
V = IGRm + IGRG
10 = 50x10-6
xRm + 50x10-6
x1000
Rm =
ଵ଴ି଴.଴ହ
ହ଴୶ଵ଴షల
‫׵‬ Rm = 200,000 Ω Ans
F
RGIG
Rm
VG
G
Vm
F F V
RG = 1000 Ω
IG = 50 ߤA Rm = ?
VG
G
Vm
V

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

28. F ˆ F www.schoolDD.com 27
N
S
E = I (r + RX + RG + R0)
I =
୉
ሺ୰ା ୖ౔ା ୖృା ୖబሻ
- 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
3. F F 2
- F F F
- F F
F
S N N S
N S S N
S N S N
F

29. F ˆ F www.schoolDD.com 28
F (magnetic field)
F F F F
F F F F
- F F F F F
- F F F F F
F
ˈ F F F F F F
ˈ F F F F F F F F F
F F F F F F F F F F F
F
N N
S
N
F
S
N
F F
x F F F F
‫׵‬ ˈ F F ˈ F
F F

30. F ˆ F www.schoolDD.com 29
F F
F F ߔ F F F
F ˈ F (Wb)
F F F F B F F F F
F ˈ F F (T)
F 18
F F 5 x 10- 4
F F F 10 F F
F F F
F ˂ F
˂ F F F
F F F F
B =
ࢶ
‫ۯ‬
Φ = 5x10-4
Wb
A = 10x10-4
m2
A (m2
)
S N
F F ߔ (Wb)
B =
ః
୅
=
ହ୶ଵ଴షర
ଵ଴୶ଵ଴షర
‫׵‬ B = 0.5 T Ans
Fv+q
F F
F
v
+q
F

31. F ˆ F www.schoolDD.com 30
F F F
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 19
-1.6x 10-19
F F 1.0x 107
F F
F F 5.0 x10 -3
F
F F
F = qvB
F
B
v
+q
90°
F
B
v
-q
90°
F
Bv
v-q
˂ ˂
F = qvB
=
‫׵‬ F = Ans

32. F ˆ F www.schoolDD.com 31
F ˂ F F F
˂ F F F F F
˂ F
F F F F =
qvB F F
F F F
F = qvB ---1
˂ I =
୯
୲
q = It
v =
ୱ
୲
=
ℓ
୲
F q v 1
F F = It(
ℓ
୲
) B
F = F (N)
I = ˂ F (A)
ℓ = (m)
B = F (T)
(F) F F F F
F ˂ F
F ˂ ( +) F
B
IN
S
ℓ
F
BI
N
S
F ˂ F F F
F = IरB

33. F ˆ F www.schoolDD.com 32
F 20
20 50 F 2 F ˂ 10
F F F F F ( F F F
)
16.7.2 ˂ F F
. F
F ˂ F F F F
F F ˂
F
I
B
I
B
F
BI
90°
F
B
I
ℓ = 0.2
F
B = 2 T
I = 10 A
N
S
F = IℓB
= 10x0.2x2
F = 4 N
F F 2
∑ F = ma
4 = 50x10-3
xa
a =
ସ
଴.଴ହ
‫׵‬ a = 80 m/s2
Ans
F F

34. F ˆ F www.schoolDD.com 33
. F F
F ˈ ˈ F F F ˂ F F
F F F F F F F F
˂ F F F F ˈ F ˂ F F ˂ F F
F
I
B
I
I
B
I
F F F
F F
I
B
B
N S
I

35. F ˆ F www.schoolDD.com 34
16.7.3 F F ˂ F
F 2 F F F ˂ F
F F F ˂ F F F
F ˂ F F F 1 F B1
F 2 F F B1 F12 F F 2
2 F B2 F 1 F
F B2 F21 F F 1
F F F ˂ F F ˈ
F ˂ ˈ
16.7.4 F ˂ F F F
F F F ˂ F
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 . I

36. F ˆ F www.schoolDD.com 35
F F F = IℓB = IbB F F
F ˈ F F F F F
F F PS QR = a
F PQ SR = b
F F F
F F = x F
M = F (a cosθ) = IbB (a cosθ)
M = IAB cosθ ( A = axb = )
F N F
M = NIAB cosθ
F Mmax cosθ = 1 θ = 0°
Mmin cosθ = 0 θ = 90°
F 21
F 1000 F 5 8 F
F 1 F ˂ 2 F F F F
60 F
b
a
S
RQ
P
I
I
I
BB
F
F
a cosθ
F
F
a
S
θP
B

37. F ˆ F www.schoolDD.com 36
16.8 F ˂
F ˂ ˈ F ˂ ˈ
F F F ˂ F F F
F ˂
. ˂ F PQRS F F F
F F
F F F a b F x y F y
x F ˂ SRQP F F
F F .
- F F F F F F
(M=0) F ( M = F (a cosθ))
a cos60
F
F
a = 0.05
60°
B = 1 T
y x
ba
P
QR
S
I
I
I BB
F
F
N S
F F M = F (a cos60)
= IℓB (a cos60)
= 2x0.08x1.0x (0.05x0.5)
= 4x10-3
N
N = 1000
M = NM = 1000x4x10-3
‫׵‬ M = 4.0 N-m Ans
F F ˂
yx
ba
F
S
RQ
P
I
I
I BB
F
F
N S
. .