6 Power in DC Circuits
Name
Date
Class
READING
Text, Sections 3-3 through 3-6
OBJECTIVES
After performing this experiment, you will be able to:
1. Determine the power in a variable resistor at various settings of resistance.
2. Plot data for power as a function of resistance. From the plot, determine when maximum power is
delivered to the variable resistor.
MATERIALS NEEDED
One 2. 7 kfl resistor
One 10 kfl potentiometer
SUMMARY OF THEORY
When there is current through a resistor, electrical energy is converted into heat. Heat is then radiated
from the resistor. The rate that heat is dissipated is called power. Power is measured in units of joules per
second (J/s), which defines the unit called the watt (W). The power dissipated by a resistor is given by the
power law equation:
P=IV
By applying Ohm's law to the power law equation, two more useful equations for power can be found.
These are:
P=PR
and
v2
1=-
R
The three power equations given above are also known as Watt's law. In this experiment, you will
determine power using the last equation. Notice that if you measure the voltage in volts (V) and the
resistance in kilohms (kfl), the power will have units of rnilliwatts (mW).
The physical size of a resistor is related to the amount of heat it can dissipate. Therefore, larger
resistors are rated for more power than smaller ones. Carbon composition resistors are available with
standard power ratings ranging from 118 W to 2 W. For most typical low voltage applications ( 15 V or less
and at least 1 kfl of resistance), a 114 W resistor is satisfactory.
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PROCEDURE
1. Measure the resistance of R 1 • The color-code value is 2.7 kO. R 1 = ____
2. Construct the circuit shown in Figure 6-l(a). Figure 6-l(b) shows an example of the circuit
constructed on a protoboard. R 2 is a 10 kO potentiometer. Connect the center (variable) terminal
to one of the outside terminals. Use this and the remaining terminal as a variable resistor. Adjust
the potentiometer for 0.5 kO. (Always remove power when measuring resistance and make
certain you are measuring only the potentiometer's resistance.)
............
...........
"'
To
power
Rz
lOkll
supply
................
................
••••••••••••••••
................
Make sure that
each leg of the
potentiometer is in
potentiometer
.... ..... .... a separate vertical
column on the
proto board.
(a) (b)
Figure 6-1
3. Use Ohm's law to compute the total current in the circuit. The total voltage is + 12.0 V. The total
resistance is R 1 + R 2 . Enter the total current in Table 6-1. The first entry has been completed as
an example.
Table &-1
Variable
VT
Resistance I=-
T R
v, v2 Power in R2 :
Setting (R 2 ) T (measured) (measured) p2
0.5k!1 3.75 rnA
l.Okfl
2.0k!1
3.0k!1
4.0k!1
5.0k!1
7.5k!1
10.0 kfl
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4. Measure the voltage across R 1 and the voltage across R 2 • Enter the measured voltages in Table
6-1. As a check, make sure that the sum of V1 and V2 is equal to 12.0 V. Then compute the power
in R 2 using either of the following equations:
or
Enter the computed power, in milliwatts, in Table 6-1.
5. Disconnect the power supply and set R 2 to the next value shown in Table 6-1. Reconnect the
power supply and repeat the measurements made in steps 3 and 4. Continue in this manner for
each of the resistance settings shown in Table 6-1.
6. Using the data in Table 6-1, graph the relationship of the power, P 2 , as a function of resistance R2
on Plot 6-1. Since resistance is the independent variable, plot it along the x-axis and plot power
along the y-axis. An implied data point can be plotted at the origin because there can be no power
dissipated in R 2 without resistance. A smooth curve can then be drawn to the origin.
Plot 6-1
CONCLUSION
EVALUATION AND REVIEW QUESTIONS
1. Observe the graph of resistance versus power for your experiment. Compare the resistance of R 1
and R 2 when power in R 2 is a maximum.
2. What was happening to the total current in the circuit as R 2 was increasing?
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3. What was happening to the power in R 1 as the resistance of R2 was increasing? Explain your
answer.
4. A 1.5 kfl resistor is found to have 22.5 V across it.
(a) What is the current in the resistor? _ _ _ _ __
(b) What is the power dissipated in the resistor? _ _ _ _ __
(c) Could a 114 W resistor be used in this application? Explain your answer.
5. What physical characteristic determines the power rating of a resistor?
6. What happens to electrical energy in a resistor?
FOR FURTHER INVESTIGATION
Because it is a series circuit, the current was the same throughout for each setting of R2 . Find the current
for each row in Table 6-1 by dividing the measured value of V1 by the measured value of R 1 • Plot this
current as a function of R2 . On the same graph, plot V2 as a function of R2 • What is the shape of the
product of these two lines?
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