University of Southeastern Philippines
College of Engineering
Physics2_ _2nd Semester SY 2017-2018
MW 11:30-1:00 pm, Rm 306
Electric Current and Resistance
University of Southeastern Philippines
COLLEGE OF GOVERNANCE AND BUSINESS
Presentation Outline
o Current, Resistance, and Electromotive Force
o Direct-current circuit
o Kirchhoff’s Rules
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Electric Current, (I )
Mathematically expressed as:
• Charges move in a direction
perpendicular to a surface
area.
o Current is a scalar quantity
o SI unit , Coulomb per second (Ampere)
1 A = 1 C/s
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Units of Current
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• In electrostatics, where charges are stationary, the electric
potential is the same everywhere in a conductor.
• In moving charges ( positive or negative) – referred as
charge carriers.
o as charges move along the wire, the electric potential is
continually decreasing.
oDecreasing electric potential means that the moving
charges lose energy.
oIf q is positive, then ∆V is negative
o in a circuit, positive charges move from regions of high
potential to regions of low potential.
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Current and Drift Speed
• Current depends on the average speed of the charge
carriers in the direction of the current, the number of
charge carriers per unit volume, and the size of the
charge carried by each.
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Mobile charge , ∆Q = number of carriers x charge per carrier
Thus : No. of mobile charge
carriers per unit volume
Drift speed ( average
speed of carriers)
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Current and Drift Speed
Direction of E is
from the positive
end of the
conductor to its
negative end.
F = -e E
If m is mass of electron, then acceleration Direction electric
produced is given by force is opposite
to the direction
of E
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Current density ,J, in a conductor
is the per unit cross- sectional area
depends on the electric field E and on the properties of the
material.
is directly proportional to E, and the ration of E to J is constant
for some metals especially metals.
Determines how dense is the current
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Resistance and Ohm’s Law
Resistance, R, is the ratio of the voltage across the conductor to the
current it carries.
Mathematically expressed as:
SI unit of R:
volts per ampere , called ohms (Ω)
Resistance in a circuit arises due to collisions between the
electrons carrying the current with fixed atoms inside the conductor.
The voltage , V, across a resistor is proportional to the current, I, that
flows through it. In general, resistance does not depend on the voltage.
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Ohm’s Law
• States that the resistance remains constant over a wide
range of applied voltages or currents.
Mathematical equation: ∆V = I R
R is the potential drop across the resistor
I is the current in the resistor
• Material that obeys ohm’s law is called an ohmic conductor or a
linear conductor.
• Materials that do not obey Ohm’s law is called nonohmic or
nonlinear .
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Resistivity, ρ
• Resistivity of a material is a measure of how strongly a
material opposes the flow of electric current.
• Is the ratio of electric field to the current density.
Unit of Resistivity: Ω. m
Mathematical
Equation:
Or Length of conductor
Cross-sectional area
The greater the resistivity, the greater the field needed to
cause a given current density, or
the smaller the current density caused a given field.
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Resistivity, ρ
• A “perfect” conductor , have ZERO RESISTIVITY, example:
metals and alloys
• “Perfect insulator, have INFINITE RESISTIVITY;
resistivity's of insulator is greater than those of metals
by enormous factor, of the order 10 22.
examples: ceramic and plastic
• Semiconductors, have INTERMEDIATE resistivity between
those of metals and those of insulators.
resistivity decreases rapidly with increasing temperature.
For Carbon ( nonmetal) decreases with increasing
temperature, and its temperature coefficient of resistivity is
negative
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Sample Problem
• a. Calculate the resistance per unit length of a 22-gauge
Nichrome wire of radius 0.321 mm.
• b. If a potential difference of 10.0 V is maintained across a
1.00-m length of the Nichrome wire, what is the current in
the wire?
• The wire is melted down and recast with twice its original
length. Find the new resistance RN as a multiple of the old
resistance Ro.
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Solution
Given : 22 gauge Nichrome wire Required:
r =0.321 mm a. Resistance per length, R
∆V = 10.0 V b. Current, I
l = 1.00 m c. new resistance , RN if new
length is twice the old length
Solution:
a. Calculate resistance per length: b. Calculate current in a 1.00 m
segment of the wire
∆V = I R Ohms law eqn.
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Temperature Variation of Resistance
• Resistivity depends upon temperature.
Resistivity of the metallic conductor always increases with
increasing temperature
Temp. coefficient of resistivity, C 0-1
Resistivity of metal
Temperature coefficient of resistivity
Equation
Reference temp. 0C
or
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Sample Problem
• A resistance thermometer, which measures temperature by
measuring the change in resistance of conductor is made of
platinum and has a resistance of 50.0Ω at 20.0 0C.
a. When the device is immersed in a vessel containing melting
indium, its resistance increases to 76.8 Ω. From this
information, find the melting point of indium.
b. The indium is heated further until it reaches a temperature
of 235 0C. What is the ratio of the new current in the platinum
to the current I mp at the melting point?
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Solution
b. ∆V = I R
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Resistor
Resistor
is a conductor that
provides a specified
resistance in an
electric circuit.
a circuit device
made to have a
specific value of
resistance
Symbol of resistor in a
circuit diagrams
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Symbols used in circuit diagram
Ammeter – used to measure current through it
Voltmeter – measures the potential difference between terminals
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Electromotive Force and Sources
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a. A circuit consisting of a
resistor connected to the
terminals of battery
For Complete Circuit (Close Circuit)
Thus current:
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Resistor in Series
• When two or more resistors are connected end to end.
• When two resistors R1 and R2 are connected in battery the current is
the same in two resistors because any charge flows through R1
must also flow through R2.
The sum of the potential differences across the resistors is equal to
the total potential difference across the combination
Req = R1+R2+R3 +…
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Resistors in Parallel
• the potential differences across the resistors are the same
because each is connected directly across the battery terminals.
• The current are generally not the same
• The equivalence resistance of a set of resistors connected in
parallel is
Note: If R1 is greater than R2, then I1 is less than I2.
Generally, more current travels through the path with less resistance.
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Resistors in Parallel
• For Equivalent Resistance of the combination is
Ohm’s law applied to the equivalent resistor is
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Circuit Definition
Node (Junction)
any point where 2 or more circuit elements are
connected together
Branch
a circuit element between two nodes
Loop
a collection of branches that form a closed path
returning to the same node without going through any
other nodes or branches twice
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Kirchhoff's Rules
• Junction rule or Kirchhoff’s Current Law (KCL)
The sum of the magnitudes
of the currents entering any
junction (node) equals the
sum of the magnitudes of the
currents leaving out of the
junction.
Conservation of Charge
Whatever current enters a given point in a
circuit must leave that point because
charge can’t build up or disappear at a
point.
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Kirchhoff's Rules
Loop rule or Kirchhoff’s Voltage Law (KVL)
The sum of the potential differences (voltage) across
all the elements (resistor or battery) around any closed
circuit loop must be zero.
R1 R2
1
+ - + -
I1 I2
E
+E – I1R1 –I2R2 = 0
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KCL and KVL
KCL at junction A: I1 + I2 –I3 = 0
KVL at loop 1: +V1 - I1R1 - I3R3 = 0
KVL at loop 2: +V2 –I2R2 - I3R3 = 0
KVL at loop 3: + V1 – I1R1 + I2R2 –V2 = 0
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• NOTE:
In KCL analysis: consider the directions of currents only
In KVL analysis: Consider the direction of assigned loop only
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Sample Problem 1
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Solution
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Problem
• Charging a battery
a. determine unknown emf of the run-down battery
b. determine internal resistance r of the 12V power supply
c. determine the unknown current I
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Solution
• a. determine unknown emf of the run-down battery
• Junction rule at point a
+2A+1A-I=0 I=3A
b. determine internal resistance r of the 12V power supply
• Loop rule for outer loop 1:
12V 3 A r 2 A 3 0 r 2
c. determine the unknown current I
• Loop rule for loop 2:
E 1V 6V 0 E 5V
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