Internal resistance of a voltage source
Electronics
Internal resistance of a voltage source
Terry Sturtevant
Wilfrid Laurier University
June 13, 2014
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
power supplies
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
power supplies
function generators
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
power supplies
function generators
amplifiers
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
power supplies
function generators
amplifiers
logic gates
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
power supplies
function generators
amplifiers
logic gates
and so on
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
Any device which produces a voltage output has a limit to the
current it can provide.
This includes
batteries
power supplies
function generators
amplifiers
logic gates
and so on
This can be represented as a resistance in series with the ideal
voltage output of the device.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
ri
6
V0
VT
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
ri
6
V0
VT
“ideal”
voltage
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
ri
internal resistance
6
V0
VT
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
ri
6
V0
VT
terminal
voltage
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
ri
6
V0
VT
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
The potential difference between the terminals of a battery,
VT , decreases as the current supplied by the battery increases.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
The potential difference between the terminals of a battery,
VT , decreases as the current supplied by the battery increases.
This is due to the potential drop which appears across the
battery’s internal resistance ri .
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
The potential difference between the terminals of a battery,
VT , decreases as the current supplied by the battery increases.
This is due to the potential drop which appears across the
battery’s internal resistance ri .
Thus the maximum potential difference is attained only with
zero output current.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
We can see the effect of this by watching how the measured
voltage changes if we put a resistance across the terminals of the
device.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
ri
6
V0
VT
R
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Notice that what we’ve done is to create a voltage divider with ri
and R.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
ri
V0
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
ri
6
V0
VT
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
ri
6
V0
VT
R
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
ri
I
6
V0
VT
R
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
ri
I
6
V0
VT
VT = V0
R
R+ri
R
?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
VT = V0
Terry Sturtevant
R
R + ri
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
VT = V0
VT
=
V0
Terry Sturtevant
R
R + ri
R
R + ri
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
VT = V0
R
R + ri
VT
=
V0
R
R + ri
V0
=
VT
R + ri
R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
VT = V0
R
R + ri
VT
=
V0
R
R + ri
V0
=
VT
R + ri
R
V0
ri
=1+
VT
R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
VT = V0
R
R + ri
VT
=
V0
R
R + ri
V0
=
VT
R + ri
R
V0
ri
=1+
VT
R
V0
ri
−1=
VT
R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Theory
Example
Internal resistance of a voltage source
VT = V0
R
R + ri
VT
=
V0
R
R + ri
V0
=
VT
R + ri
R
V0
ri
=1+
VT
R
V0
ri
−1=
VT
R
ri =
V0
−1 R
VT
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
So if we can measure the voltage with no load; (i.e.
essentially V0 ), and then the voltage VT with some resistance
R, then we can determine ri .
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
So if we can measure the voltage with no load; (i.e.
essentially V0 ), and then the voltage VT with some resistance
R, then
we can
determine ri .
ri =
V0
VT
−1 R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
So if we can measure the voltage with no load; (i.e.
essentially V0 ), and then the voltage VT with some resistance
R, then
we can
determine ri .
ri =
V0
VT
−1 R
Note that the bigger the drop with load, the bigger ri is,
which makes sense.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
So if we can measure the voltage with no load; (i.e.
essentially V0 ), and then the voltage VT with some resistance
R, then
we can
determine ri .
ri =
V0
VT
−1 R
Note that the bigger the drop with load, the bigger ri is,
which makes sense.
Question: If R is chosen to equal ri , what will be the value of
VT ?
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
To graph this, it makes sense to linearize the equation:
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
To graph this, it makes sense to linearize the equation:
V0
ri
=1+
VT
R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
To graph this, it makes sense to linearize the equation:
V0
ri
=1+
VT
R
Dividing both sides by V0 gives
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
To graph this, it makes sense to linearize the equation:
V0
ri
=1+
VT
R
Dividing both sides by V0 gives
1
1
ri
=
+
VT
V0 V0 R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
To graph this, it makes sense to linearize the equation:
V0
ri
=1+
VT
R
Dividing both sides by V0 gives
1
1
ri
=
+
VT
V0 V0 R
or
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Graphical analysis
To graph this, it makes sense to linearize the equation:
V0
ri
=1+
VT
R
Dividing both sides by V0 gives
1
1
ri
=
+
VT
V0 V0 R
or
1
1
ri 1
=
+
VT
V0 V0 R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
1
VT
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
1
VT
versus
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
1
VT
versus
1
R
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
1
VT
versus
1
R
then we will get a straight line
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
of
1
VT
versus
1
R
then we will get a straight line with a slope
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot
of Vri0
1
VT
versus
1
R
then we will get a straight line with a slope
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot V1T versus R1 then we will get a straight line with a slope
of Vri0 and a y -intercept of
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot V1T versus R1 then we will get a straight line with a slope
of Vri0 and a y -intercept of V10 .
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
1
1
ri 1
=
+
VT
V0 V0 R
If we plot V1T versus R1 then we will get a straight line with a slope
of Vri0 and a y -intercept of V10 .
We can get ri by dividing the slope by the y -intercept.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Here’s the setup:
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Here’s the setup:
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Here are the data collected for a new 9 volt battery.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
9.27
9.27
9.27
..
.
6800
3300
2200
1000
680
330
220
100
47
9.24
9.22
9.20
9.17
9.14
9.08
9.01
8.80
8.40
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
The graph of
1
VT
versus
1
R
Theory
Example
looks like this:
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit to the data gives:
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit to the data gives:
V0 = 9.246 ± 0.006V
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit to the data gives:
V0 = 9.246 ± 0.006V
Imax = 1.89 ± 0.05A
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit to the data gives:
V0 = 9.246 ± 0.006V
Imax = 1.89 ± 0.05A
ri = 4.8 ± 0.1Ω
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
Here are the data collected for a used 9 volt battery.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
External resistance R
(Ω)
∞
1000000
680000
..
.
Terminal voltage VT
(V )
7.32
7.32
7.32
..
.
6800
3300
2200
1000
680
330
220
100
47
7.11
7.01
6.93
6.71
6.56
6.10
5.72
4.71
3.55
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
The graph of
1
VT
versus
1
R
Theory
Example
looks like this:
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
0.25
0.05
0.15
0.10
0.05
0
0.005
0.000
0.015
0.010
Terry Sturtevant
0.025
0.020
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
The steeper slope of this graph compared to the last one indicates
that the internal resistance is much higher; in other words, the
output voltage changes much more as current increases compared
to the new battery.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit was produced, as before, but only the last five
points were used due to the curve at the left of the graph.
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit was produced, as before, but only the last five
points were used due to the curve at the left of the graph.
V0 = 6.78 ± 0.08V
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit was produced, as before, but only the last five
points were used due to the curve at the left of the graph.
V0 = 6.78 ± 0.08V
Imax = 0.33 ± 0.02A
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit was produced, as before, but only the last five
points were used due to the curve at the left of the graph.
V0 = 6.78 ± 0.08V
Imax = 0.33 ± 0.02A
ri = 20 ± 1Ω
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Theory
Example
A least squares fit was produced, as before, but only the last five
points were used due to the curve at the left of the graph.
V0 = 6.78 ± 0.08V
Imax = 0.33 ± 0.02A
ri = 20 ± 1Ω
(Using all of the data points gives slightly different results, but
ones that are still much different than those for the new battery.)
Terry Sturtevant
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Parameter
V0 (V )
Imax (A)
ri (Ω)
Theory
Example
New battery
9.246 ± 0.006
1.89 ± 0.05
4.8 ± 0.1
Terry Sturtevant
Old battery
6.78 ± 0.08
0.33 ± 0.02
20 ± 1
Electronics Internal resistance of a voltage source
Internal resistance of a voltage source
Parameter
V0 (V )
Imax (A)
ri (Ω)
Theory
Example
New battery
9.246 ± 0.006
1.89 ± 0.05
4.8 ± 0.1
Old battery
6.78 ± 0.08
0.33 ± 0.02
20 ± 1
Even though the nominal battery voltage is only 27% lower,
the internal resistance is 5 times as high, and the maximum
current available is only 1/6 of what it is for the new battery.
Terry Sturtevant
Electronics Internal resistance of a voltage source