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Circuit elements
Resistors
Resistance

The electrical resistance of a circuit component or device
is defined as the ratio of the voltage applied to the electric
current whichflows through it:

If the resistance is constant over a considerable range of
voltage, then Ohm's law ,I = V/R, can be used to predict
the behavior of the material.

The resistivity, and thus the resistance, is temperature
dependent
Resistivity and Conductivity

The electrical resistance of a wire would be expected to be
greater for a longer wire, less for a wire of larger cross
sectional area, and would be expected to depend upon the
material out of which the wire is made  The resistance of
a wire can be expressed as
Resistance = resistivity x length/area

The factor in the resistance which takes into account the
nature of the material is the resistivity ρ .

The inverse of resistivity is called conductivity. There are
contexts where the use of conductivity is more convenient.
Electrical conductivity = σ = 1/ρ
Resistor Combinations
The combination rules for any number of
resistors in series or parallel can be
derived with the use of Ohm's Law, the
voltage law, and the current law.
Series Resistors
Series Resistors
Parallel Resistors
Parallel Resistors
Parallel
resistors

Two R’s


More than 2R’s
For I

Then R

DC Electric Power
Remember: Ohm's Law

For many conductors of electricity
 I is directly proportional to V applied to them.

The ratio of V/I is called the resistance
 and if the ratio is constant over a wide range of
voltages, the material is said to be an "ohmic" material.

If the material can be characterized by such a
resistance, then the current can be predicted from the
relationship:
DC Electric Power

The electric power in watts associated with a
complete electric circuit or a circuit component
represents the rate at which energy is converted from
the electrical energy of the moving charges to some
other form, e.g., heat, mechanical energy, or energy
stored in electric fields or magnetic fields.

For a resistor in a DC circuit the power is given by the
product of applied voltage and the electric current:
Power = Voltage x Current
P = VI
Power
Power is the rate energy is “used” (actually converted
to heat or another form). Power is measured in watts (or
kilowatts). Notice that rate always involves time.
One watt = one joule/second
Three equations for power in circuits that are
collectively known as Watt’s law are:
P  IV
PI R
2
2
V
P
R
Power Dissipated in Resistor
Convenient expressions for the power
dissipated in a resistor can be obtained
by the use of Ohm's Law.
Power
What power is dissipated in a 27 W resistor is the
current is 0.135 A?
Given that you know the resistance and current,
substitute the values into P =I 2R.
P  I 2R
 (0.135 A) 2  27 W 
 0.49 W
Power
What power is dissipated by a heater that draws 12 A
of current from a 120 V supply?
The most direct solution is to substitute into P = IV.
P  IV
 12 A 120 V 
 1440 W
Power
What power is dissipated in a 100 W resistor with 5 V
across it?
V2
The most direct solution is to substitute into P 
.
R
2
V
P
Small resistors operating in low
R
5 V


2
100 W
 0.25 W
voltage systems need to be sized
for the anticipated power.
1n
Energy
Energy, W, is the ability to do work and is
measured in joules. One joule is the work
done when a force of one newton is
applied through a distance of one meter.
The symbol for energy, W, represents
work, but should not be confused with the
unit for power, the watt, W.
1m
Energy
The kilowatt-hour (kWh) is a much larger unit of
energy than the joule. There are 3.6 x 106 J in a kWh.
The kWh is convenient for electrical appliances.
What is the energy used in operating a
1200 W heater for 20 minutes?
1200 W = 1.2 kW
20 min = 1/3 h
1.2 kW X 1/3 h =0.4 kWh