Physics 106 Lesson #15
Electrical Resistance
and Ohm’s Law
Dr. Andrew Tomasch
2405 Randall Lab
atomasch@umich.edu
Resistors
Resistors are used in appliances
to convert electrical energy into
thermal energy (heat) or light
Toaster
Space Heater
Light Bulb
When an extension cord is used
with a space heater, the cord
must have a resistance that is
sufficiently small to prevent
overheating of the cord
Stove Heating Element
Ohm’s Law
• The resistance of the
resistor (light bulb) is R
• The voltage across the
resistor is V
• The current through the
resistor is I
• Ohm’s Law:
V  IR
Ohms (W)
I
Voltage = V
R
Voltage = 0
I
Assume perfect
wire  NO voltage
drop across wires!
I
Adding Series Resistors
• For resistors R1 & R2
connected in series
(sequentially), the
current i passing
through each resistor
must be the same
• The voltages across
R1 & R2 must add up
to V → V = iR1 + iR2
= i(R1 + R2) = iReq
V
+
Req  R1  R2
Adding Parallel Resistors
• Resistors R1 & R2
connected in parallel
have the same potential
difference (voltage) V
across them
• The total current is the
sum of the current
through each resistor
• I = I1 + I2 = V/R1 + V/R2 =
V(1/R1 + 1/R2 ) = V /Req
V
+
1/ Req  1/ R1  1/ R2
More Ways to Calculate Power
• Electric Potential
Energy is transformed
into to some other
form (heat, light) by the
resistor (light bulb).
• Power:
V  IR
I V /R
2
V
P  IV  I R 
R
2
I
Voltage = V
R
Voltage = 0
I
Electric Potential
(Energy) decreases
across the light bulb
(resistor)
I
Ohm’s Law: Discussion
• Ohm’s Law states that the potential
difference across a resistor is
proportional to the current flowing
through it
• Resistance is the constant of
proportionality between current and
voltage
• Ohm’s “Law” is not a law at all—it is a
definition. Semiconductor devices
(diodes, transistors) are useful because
they do not obey Ohm’s “Law”
Superconductivity: Zero Resistance
• The resistance of many (but
not all) substances
decreases with temperature
• A special class of materials
known as superconductors
lose all electrical resistance
below a temperature known
as the critical temperature
• Superconductors can
levitate magnets by the
Meissner Effect where a
perfect conductor expels all
magnetic fields from its
interior
Demonstration
Using Superconductivity
SMILI 1989
HEAT-pbar
Powerful
superconducting
electromagnets,
cooled with
liquid Helium,
produce intense
magnetic fields
that can be used
to measure the
momentum of
charged Cosmic
Ray particles
(atomic nuclei)
produced by
supernova
explosions in the
galaxy.
Superconducting
Magnet
HEAT-pbar 2000