CHAPTER VII DIRECT CURRENT CIRCUITS
CHAPTER VII
DIRECT CURRENT CIRCUITS
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 ).
t
qi
e
qn n = the amount of electron
e = the electron charge/the elementary charge
= 1,6 x 10 -19 C
i = Electric current ( ampere )
q = charge ( coulomb )
t = unit of time ( second )
Direct current
source
Direction of electric
current
Direction of moving
electrons
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)
A = Cross-section Area ( m2)
L = Length (m)ΑR
ρ
MATERIALSRESISTIVITY
ρ(Ωm)
TEMPERATURE
COEFFICIENT(1/OC)
Silver
Copper
Gold
Aluminum
Tungsten
Iron
Platinum
Lead
Nichrome
Carbon
Germanium
Silicon
Glass
1,59 x 10-8
1,7 x 10-8
2,44 x 10-8
2,82 x 10-8
5,6 x 10-8
10 x 10-8
11 x 10-8
22 x 10-8
1,50 x 10-6
3,5 x 10-5
0,46
640
1010 - 1014
3,8 x 10-3
3,9 x 10-3
3,4 x 10-3
3,9 x 10-3
4,5 x 10-3
5,0 x 10-3
3,92 x 10-3
3,9 x 10-3
0,4 x 10-3
-0,5 x 10-3
-48 x 10-3
-75 x 10-3
Resistivities and TemperaturecCoefficients of Resistivity fo
various Materials
Temperature Influence for resistivity and
resistance
).1( TRR ot
If temperature of wire is increase, so the resistivity and the resistance of it is
increase
or TRR O ..
).1( Tot TO ..or
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
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)
R = tan α
A = Ammeter
V = Voltmeter
L = Lamp
A
V
L
V
V
i
Graph of V - i
i = Current (A)
V = Voltage/the potential difference (V)
R = Resistance (Ω)
RiV Ri
V
MEASUREMENT OF CURRENT
AND VOLTAGE
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 :
I1
i5i6
I2 i3
i4
i1 + i2 + i4 = i3 + i5 + i6
SERIES CIRCUIT (VOLTAGE DIVIDER)
i1 = i2 = i3 = I
RS = R1 + R2 + R3
V = V1 + V2 + V3
V1 : V2 : V3 = R1 : R2 : R3
Characteristic :
The current passing
through every resistor is
equal.
The potential difference
on every resistor is
different.
VR
RV
S
11 V
R
RV
S
22 V
R
RV
S
33
SRIV
V
R1 R2 R3
I
PARALLEL CIRCUIT (ELECTRIC CURRENT DIVIDER)
R3
1:
R2
1:
R1
1i:i:i
VV 3V 2V 1
3 R
1
2R
1
1R
1
R
1
iiii
321
P
321
Characteristics :
The current passing
through the junction is
different.
The potential difference
of every junction is
equal.
i3
R3
R1
R2
i1
i2i
V
IR
Ri
p
1
1I
R
Ri
p
3
3
pR
VI I
R
Ri
p
2
2
If in the galvanometer
(G) there are no electric
current passed, called a
galvanometer in
equilibrium condition
E. WHEAT STONE’S BRIDGE
Conducting wire
G
R2
LA LB
R1
R1 . RB = R2 . RAΑ
R
ρ
R1 . LB = R2 . LA
because
so;RA= wire resistance of part A
RB= wire resistance of part B
LA= wire length of part A
LB= wire length of part B
The forms of Wheat stone bridge:
R1 . R3 = R2 . R4
R1
R2
R3
R5R4
R4
R1 R2
R3
R5
R1 R2
R4
R5
R3
@
@
@
If:
so, R5 can be ignored
and then the wheat stone bridge circuit
can be simplified to:
R4
R1 R2
R3
R1 . R3 ≠ R2 . R4 Ifso, the circuits can be transforms to form Y (transformation of ∆ to
Y )
R4
R1R2
R3
R5
Ra
Rb
Rc
R2
R3
Ra
Rb
Rc
541
41aR
RRR
RR
541
51bR
RRR
RR
541
54cR
RRR
RR
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)
ε
r
i
R
V
K
• 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
ε= EMF (volt)
r = internal resistance (Ω )
R = external resistance (Ω )
ε = i R + i r ε = i ( R + r )
If the batteries are identical, and
each has an EMF ε, and an
internal resistance r
Series Connection of Batteries
R
ε1 ε2 ε3
r1 r2 r3
Σε = n ε
Σr = n r
i
Σε = ε1 + ε2 +ε3
Σr = r1 + r2 + r3
r3
r1
r2
Parallel Connection of Batteriesε1
ε2
ε3
Σε = ε
For identical batteries:
i
R
Compound Connection of BatteriesE1
r1
E2
r2
E3
r3
E4
r4
E5
r5
E6
r1
E7
r2
E8
r3
E9
r4
E10
r5E11
r11
E12
r12
E13
r13
E14
r14
E15
r15
G. KIRCHHOFF’S SECOND RULES
or Σε = Σ (i. R)
Σ(i.R) = Dropping Potential difference
ε = EMF ( electromotive force )
Σε + Σ (i . R) = 0
The sum of the drops in potential difference in a close circuit is
equal to zero.
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
G. WORK DONE BY THE ELECTRIC CURRENT ( JOULE’S LAW)
W = q V
W = electrical energy (J)
V = potential difference (volt)
q = charge (C)
i = electric current (A)
t = time ( s )
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
Since q = i t, W = V i t
And V= I R W = i2 R t
R
V i
W = i2 R tR
V W
2
t
W P
P = Electric Power (Watt)
The electrical energy dissipated per unit time (second) is called electrical power.
t
ti V P i V P
t
Rti P
2
R2i P
t
tR
V
P
2
R
V P
2