The internal resistance of the voltage source
The internal resistance Ri of a voltage source is to be
examined by measuring the current and the voltage across
the terminals under different loads.
Equipment
Physics demonstration board, with frame
Connector, straight, module DB
Connector, angled, module DB
Connector, T-shaped, module DB
Connector, interrupted, module DB
Switch on/off, module DB
Battery box
Resistor 1 Ω, module DB
Resistor 10 Ω, module DB
Resistor 50 Ω, module DB
Electr. symbols f. demo-board, 12 pcs
Connecting cable, 100 cm, red
Connecting cable, 100 cm, blue
Analog demonstration multimeter ADM 2
Battery, 1.5 V, R14
02150.00
09401.01
09401.02
09401.03
09401.04
09402.01
05605.00
09411.10
09412.10
09412.50
02154.03
07363.01
07363.04
13820.00
07922.01
1
1
4
2
3
1
1
1
1
1
1
2
2
2
2
ET
2.9
Set-Up and Procedure
— Connect up the circuit as shown in Fig. 1, first using
resistor R1 = 50 Ω; select the 3 V- and 100 mA- measurement ranges.
— With the switch open, measure the terminal voltage UT
for IL = 0, i.e. without a load on the voltage source;
enter the measured value in Table 1.
— Close the switch, read off the terminal voltage UT and
current IL (under load); note the measured values.
— Change to the 300 mA- measurement range; replace
resistor R1 = 50 Ω with resistor R2 = 10 Ω; measure UT
and IL and note the measured values.
— Change to the 3 A- measurement range; replace resistor R2 = 10 Ω with resistor R3 = 1 Ω ; measure UT and IL
and note the measured values.
— Finally, with the switch open (!), replace resistor R3 by
the straight connector module.
— Briefly (!) close the switch and, during the short circuit,
measure UT and IL; note the measured values.
Fig. 1
Phywe series of publications • Demon. Exp. Physics • Electricity/Electronics on the Magnetic Board 1 • © PHYWE SYSTEME GMBH • D-37070 Göttingen
13818
39
ET
2.9
The internal resistance of the voltage source
The internal resistance can be determined from the slope
of this load line:
Measurement Results
Table 1
Resistance
R/Ω
Load current
IL/A
Ri = ∆UT/ ∆IL.
Terminal voltage
UT /V
0
1.53
50
0.029
1.48
10
0.13
1.43
1
0.77
0.95
0
1.62
0.37
Evaluation
The terminal voltage UT of the voltage supply decreases
with increasing load, i.e. with increasing (load) current IL.
This indicates that the voltage supply has a resistance.
This resistance is called the internal resistance Ri.
The load current IL effects a voltage drop Ri · IL at the
internal resistance Ri so that the terminal voltage drops to
For the battery used in this experiment, we have from
Fig. 2:
Ri = ∆UT/ ∆IL ≈ 0.5 V/0.7 A = 0.71 Ω.
Remarks
Commercially available dry batteries are very suitable for
the examination of internal resistance. Their internal resistance is high enough to be measurable, and they are easily replaceable should they be damaged by overloading for
too long.
The power supply is not suitable for this examination of
internal resistance, because it is voltage stabilized.
Voltage sources used in practice differ in their internal
resistances. The value of Ri must be very low for a car battery, for example, for sufficient current to be supplied to
start up the motor.
UT = U0 – Ri · IL
Fig. 2
U0 is the terminal voltage of the voltage source without
load, the source voltage.
Using Ri · IL = Ui, then
UT = U0 – Ui or
U0 = UT + Ui.
When the resistance in the outer circuit Ra is known, then
R0 = Ra + Ri is true, i.e each circuit is a series connection
of Ri and the resistance in the circuit Ra.
A graphical representation of the resistance in the outer
circuit Ra in dependence on the load current (Fig. 2) shows
a linear function with negative slope. The larger the internal resistance of the voltage source, the steeper the slope
of the straight line, i.e. the larger the drop in the terminal
voltage under increasing load.
40
13818
Phywe series of publications • Demon. Exp. Physics • Electricity/Electronics on the Magnetic Board 1 • © PHYWE SYSTEME GMBH • D-37070 Göttingen