1. Electric current is defined as the amount of charge passing through a conductor per unit time. It is measured in amperes and represented by the letter i. 2. The resistance of a conductor depends on its length, cross-sectional area, material, and temperature. Resistance is measured in ohms and represented by R. Resistance increases with length, decreases with area, and increases with temperature. 3. Ohm's law states that the current through a conductor is directly proportional to the voltage applied and inversely proportional to the resistance of the conductor. It is represented by the equation V=IR.

1. CHAPTER VII
DIRECT CURRENT CIRCUITS

2. A. DEFINITION OF ELECTRIC CURRENT
Electric current illustrated as a motion of positive charges
passing through from the higher potential to the lower
potential.
Electric current (i) defined as the amount of charge
passing through in every unit of time ( second ).
q i = Electric current ( ampere )
i  q = charge ( coulomb )
t t = unit of time ( second )
q
n  n = the amount of electron
e e = the electron charge/the elementary charge
= 1,6 x 10 -19 C

3. Direction of electric
current
Direction of moving
electrons
Direct current
source

4. B. RESISTANCE OF CONDUCTING WIRE
The resistance of a conducting wire depends on :
 Length of the wire
 Cross section Area
 Kind of the wire
 Temperature
Formula :
R = Resistance ( Ohm, Ω )
 ρ = Resistivity of the material ( Ω m)
Rρ A = Cross-section Area ( m2)
Α L = Length (m)

5.  Resistivities and TemperaturecCoefficients of Resistivity fo
various Materials
RESISTIVITY TEMPERATURE
MATERIALS
ρ(Ωm) COEFFICIENT(1/OC)
Silver 1,59 x 10-8 3,8 x 10-3
Copper 1,7 x 10-8 3,9 x 10-3
Gold 2,44 x 10-8 3,4 x 10-3
Aluminum 2,82 x 10-8 3,9 x 10-3
Tungsten 5,6 x 10-8 4,5 x 10-3
Iron 10 x 10-8 5,0 x 10-3
Platinum 11 x 10-8 3,92 x 10-3
Lead 22 x 10-8 3,9 x 10-3
Nichrome 1,50 x 10-6 0,4 x 10-3
Carbon 3,5 x 10-5 -0,5 x 10-3
Germanium 0,46 -48 x 10-3
Silicon 640 -75 x 10-3
Glass 1010 - 1014

6. Temperature Influence for resistivity and
resistance
If temperature of wire is increase, so the resistivity and the resistance of it is
increase
Rt  Ro (1   .T ) or R  RO . .T
t   o (1   .T ) or    O . .T
ρO = initial of resistivity (Ωm)
ρt = final of resistivity (Ωm)
Ro = initial of resistance(Ω)
Rt = final of resistance (Ω)
ΔT = the change of temperature (oC)
α = temperature coefficient of resistivity (/ oC)
∆R = The change of resistance
∆ρ = The change of resistivity

7. C. OHM’S LAW
The ratio of the voltage (V) across a conductor to the
current (i) that flows through it is equal to a constant.
This constant is called resistance (R)
V
V
i
R V  iR A
L
A = Ammeter
V = Voltmeter
L = Lamp
i = Current (A) V
V
V = Voltage/the potential difference (V)
R = Resistance (Ω)
R = tan α
 i
Graph of V - i

8. MEASUREMENT OF CURRENT
AND VOLTAGE

9. D. SERIES AND PARALLEL CIRCUIT
Kirchhoff’s first rule:
The sum of the currents entering the any
junction must equal the sum of the currents
leaving the junction.
Example : i5
i6
I1
i4
I2 i3
i1 + i 2 + i 4 = i3 + i5 + i6

10. SERIES CIRCUIT (VOLTAGE DIVIDER)
R1 R2 R3
Characteristic :
I
 The current passing
V
through every resistor is
equal.
i1 = i2 = i3 = I  The potential difference
RS = R1 + R2 + R3
on every resistor is
different.
V = V1 + V2 + V3
V1 : V2 : V3 = R1 : R2 : R3
V  I  RS
R1 R2 R3
V1  V V2  V V3  V
RS RS RS

11. PARALLEL CIRCUIT (ELECTRIC CURRENT DIVIDER)
R1
i1
i
Characteristics :
i2 R2
 The current passing
i3 through the junction is
R3
different.
V
 The potential difference
i  i1  i 2  i 3 of every junction is
1 1 1 1 equal.
  
RP R R R
1 2 3
V1 V 2 V 3 V
1 1 1
i1 : i 2 : i 3  : :
R1 R 2 R 3
Rp Rp Rp V
i1  I i2  I i3  I I 
R1 R2 R3 Rp

12. E. WHEAT STONE’S BRIDGE
If in the galvanometer R1 R2
(G) there are no electric G
current passed, called a LA LB
galvanometer in Conducting wire
equilibrium condition
R1 . R B = R2 . R A because 
R ρ
Α
so;
RA= wire resistance of part A
R1 . L B = R2 . L A RB= wire resistance of part B
LA= wire length of part A
LB= wire length of part B

13. The forms of Wheat stone bridge:
R1 R2 If:
@ R5 R 1 . R3 = R 2 . R 4
R4 R3 so, R5 can be ignored
and then the wheat
R1 R2 stone bridge circuit
can be simplified to:
@ R5
R4 R3
R1 R2
R1
R4 R3
R4 R5 R2
@
R3

14. If R1 . R3 ≠ R2 . R4
so, the circuits can be transforms to form Y (transformation of ∆ to
Y)
R1 R2 R2
Rb Rb
R5
Ra Ra
Rc Rc
R3 R3
R4
R1  R4 R4  R5
Ra  Rc 
R1  R4  R5 R1  R4  R5
R1  R5
Rb 
R1  R4  R5

15. F. SOURCE OF ELECTROMOTIVE FORCE (EMF)
Current in conductor is produced by an electric field, and
electric field is formed by the potential difference, devices
such as batteries and dynamos should be connected to the
circuit. These sources of electric energy are called source of
electromotive force (ε)
R
K
● ●
i
ε
r
V
• When the switch K is open, the voltmeter reads is EMF (ε)
• When the switch K is closed, the voltmeter reads is clamping voltage (V)
V= i R V= clamping voltage = potential difference on the
external resistance

16. ε=iR+ir ε=i(R+r)
ε = EMF (volt)
r = internal resistance (Ω )
R = external resistance (Ω )
Series Connection of Batteries
ε1 ε2 ε3
Σε = ε1 + ε2 +ε3
r1 r2 r3
i
Σr = r1 + r2 + r3
R
If the batteries are identical, and
each has an EMF ε, and an Σε = n ε
internal resistance r
Σr = n r

17.  Parallel Connection of Batteries
ε1
r1
ε2
r2
ε3
i
r3
R
For identical batteries:
Σε = ε

18.  Compound Connection of Batteries
E1 E2 E3 E4 E5
r1 r2 r3 r4 r5
E6 E7 E8 E9 E10
r1 r2 r3 r4 r5
E11 E12 E13 E14 E15
r11 r12 r13 r14 r15

19. G. KIRCHHOFF’S SECOND RULES
The sum of the drops in potential difference in a close circuit is
equal to zero.
Σε + Σ (i . R) = 0 or Σε = Σ (i. R)
Σ(i.R) = Dropping Potential difference
ε = EMF ( electromotive force )
 In applying Kirchhoff’s rules, the following rules should be noted:
1. Assign a symbol and direction to the currents in each part of the circuit
2. Loops are chosen and the direction around each loop is designated
3. The sign of the current are taken “+” when they are in the same direction
of loops, and taken “-” when they are in the opposite direction of loops
4. The sign of the EMF are taken “+” when loops inside polar (+) of
elements, and taken “-” when loops inside polar (-) of elements

20. G. WORK DONE BY THE ELECTRIC CURRENT ( JOULE’S LAW)
The amount of heat dissipated from a current carrying
conductor is proportional to the resistance of the
conductor, the square of current and the time needed
for the current to pass trough the conductor
W=qV
V2
Since q = i t, W=Vit i
V
W
R R
And V= I R W = i2 R t
W = electrical energy (J)
V = potential difference (volt)
q = charge (C)
i = electric current (A)
t = time ( s )

21. The electrical energy dissipated per unit time (second) is called
electrical power.
Vi t
P PVi
t
W
P P
i 2 Rt
Pi R 2
t V2
t
t
V2
P R P
t R
P = Electric Power (Watt)