Transcript No Slide Title

It is essential to specify reference directions for
current and voltage
i(t)
+
V(t)
-
Voltage and current are algebraic quantities and the
signs are critical.
1
Resistors are very common circuit elements
What is their function ?
2
Resistors obey Ohm’s law.
i(t)
+
v(t)
R
v(t)  i(t)R
_
Note the convention on reference directions:
For passive elements, current flows into the positive terminal
3
For passive elements, current flows into the positive
terminal
i(t)
_
v(t)
R
v(t)  i(t)R
+
4
In a resistor, voltage is directly proportional
to current
v(t)  i ( t ) R
v
R = slope
i
5
Ohm’s law in action: example
v(t)  i ( t ) R
V
2
R = 1kW
1
1
2
3
i (mA)
6
A resistor can also be characterized by a quantity
called conductance (G).
i
i(t) = G v(t)
G = slope
1
G =
R
v
W
1
-1
Unit of G is mho 
W 
W
7
Resistance can be readily calculated for geometric
figures with constant cross-section
L
s
A
L
R =
sA
s = Conductivity
( Wm )
L = Length of the cylinder ( m )
A = Area of the cylinder
( m2 )
The units of resistance is ohms (W).
8
Resistance is proportional to length
and inversly proportional to the cross sectional area
L
A
s
Long wires have large resistance
L
R=
sA
Thick cross section bars
will have low resistance
Resistance depends on the material
9
Copper wires have very low resistance
L

0.3 m
A  10-6 m2
s  5.7 107
However, if L
 3 km
L
R=
sA
R  5. 3 m W
R  53 W
10
For an ideal voltage source, voltage is independent of current
I
v(t)
+
_
V
Reference current convention of a voltage source is arbitrary
11
Examples of voltage sources
Pulsed
DC
voltage
time
AC
Ramp
12
In an ideal current source, current is independent
of voltage
i(t)
I
V
13