Chapter 6: Current, Resistance, Electromotive Forces and
Direct Current Circuits
Electric Current and Resistance
Electric circuit is being extensively used in our daily lives, in
illumination, current and etc.
In 1791, Italian Luigi Galvani (1737-1798) found a way to produce
electric current.
The first battery (Repeated stack of copper/zinc disk moistened
with salt water) was created by Count Alessandro Volta (17451827). Volta recognized the crucial difference between the
electricity from a battery and that from an electrostatic device such
a Layden jar.
Electromotive Force (Emf =  )
The potential difference between the terminals of a battery when
no current is present
Or
The potential difference across the terminals of a battery when it is
not connected to a circuit.
R
Electron flow

r
terminal Potenttial Difference across a resistor
TPD = – I r
Battery in series
Electron flow
Total Voltage VT = V1 + V2 + V3
Battery in parallel
The potential is the same anywhere in the circuit
Electron flow
VT= V1=V2=V3
Electric Current and drift velocity
Current is define as the rate flow of charge where current is
I=
1 Ampere
Q
t
= 1Coulomb
sec ond
Drift velocity
The net electron flow is characterized by an average velocity called
the drift velocity, which is much smaller than the random
velocities of the electrons themselves.
When a potential difference is applied, the associated electric field
in the conductor travels at the speed close to the speed of light.
Resistance and Ohm’s Law
Resistance ( R ) is define as the ratio of the voltage to the resulting
current.
The Ohm law states that Voltage (V) is proportional to current (I)
if the resistance is constant (George Ohm 1789-1851).
V= I R or R =
V
I
SI unit for resistance: volt per ampere (V/A) or ohm ()
A resistance that has a constant resistance is said to obey Ohm’s
law or to be “ohmic”.
Factor that influence resistance
The resistance is proportional to its length and inversely
proportional to it cross section A
R
L
A
Resistivity and conductivity
The resistance of a material is determine by intrinsic atomic
properties
R=
L
A
or =
RA
L
SI unit for Resistivity: ohm-meter (.m)
Conductivity is reverse of Resistivity, where
=
1

conductivity
SI unit of conductivity: inverse ohm-meter [(.m)-1]
Resistance is temperature dependence. The temperature
dependence of Resistivity is nearly linear if the temperature change
is not too great
The Resistivity () at a temperature T after a temperature change
 T = T – To is given by:
 = o (1 + T) temperature variation of Resistivity
 = o T
 =  - o
R is proportional to 
R = Ro (1 + T)
R = Ro T Temperature variation of resistance
Electric Power
Power =
W qV

t
t
P= VI =
V2
R
=I2R
1 kWh= (1000W)(3600s)=3.6 x 106J
Chapter 7: Kirchoff Rules
A general method for analyzing circuit is by using Kirchoff rules
a. Kirchoff Junction Theorem
Kirchoff junction theorem states that the algebraic sum of the
currents at any junction is zero:
iIi = 0 sum of currents at junctions
The sum of current entering the junction (taken as positive) is
equal the sum of currents leaving the junction (taken as negative).
I1 = I2 +I3
Current in = current out
b. Kirchoff Voltage Theorem
Kirchoff voltage theorem or loop theorem states that the algebraic
sum of the potential difference (voltages) across all the elements of
any close loop is zero.
iVi = 0 sum of voltage around close loop
This means that the sum of voltage rises equal the sum of voltage
drop around a close circuit.
Sign convention for Kirchoff rule
a. When Kirchoff’s rules are applied around a circuit loop, the
voltage across a battery is taken to be (+) if a battery is
traversed from the negative to the positive terminal and
negative (-) if the battery is traversed from the positive to the
negative.
b. The voltage across a resistor is taken to be (-) if the
resistance is traversed in the direction of the assigned branch
current and positive (+) if the resistance is traversed in the
direction opposite that of the assigned branched current.
Resistance in Series
R1
V1=IR1
VT
R2
V2=IR2
R3
V3=IR3
The analysis of the circuit
V - i (IRi) = 0
V=iVi = i (IRi)
For the circuit in the diagram
VT = V1 + V2 +V3
V=IR and the current I is the same anywhere in a series circuit.
RT = R1 +R2 +R3
Resistor in Parallel.
When a resistor are connected in parallel across a battery, the
voltage drop across each resistor is the same (the same as the
voltage of the battery)
IT
I3
I1
R1
R1
I2
R2
R3
IT = I1 +I2 +I3
V battery = V1 = V2 =V3
1
1
1
1



R p R1 R2 R3
Series connection provides a way to increase total resistance
Parallel connections provide a way to decrease total resistance