Kirchhoff’s Rules and Electric Power
Introduction
In part one of this lab, we test Kirchhoff’s Loop and Junction Rules. In part two, we discover how to
maximize the effective power drawn from a non-ideal battery. Text Reference: Young and Freedman
§26.2 (Part 1) and §§25.4-5 (Part 2)
Procedure: The values for R0, R1, R2, R3, V0, and V1 will be provided in class (ask your TA).
Part 1:
Set up the circuit shown below with a power supply, three resistors, and two-decade resistance
boxes; use the digital multimeter (DMM) to measure the resistances which may be slightly different
from the values of resistance as given in the figure. Note that this circuit cannot be analyzed by
means of simple rules for resistors in series and parallel. Set the output of the power supply at V0 (V)
using digital voltmeter (DVM). Use the DVM to measure the potential differences across each of the
five resistors; keep track of which side is at higher potential in each case. Test Kirchhoff’s Loop
Rule for loops abcda, dcfed, and abcfeda. Next, use the ammeter capability of the DMM to measure
the currents through each resistor; keep track of the current direction in each case. Test Kirchhoff’s
Junction rule for junctions c and d. Report the results of your five tests; be sure to report your
agreement or disagreement. Address carefully any discrepancies.
Figure 1: Circuit for part 1.
Part 2:
Set up the circuit shown on the next page with a power supply and two-decade resistance boxes. Adjust
the resistance of the internal resistor R0 and the voltage V1 from the power supply according to the
instructions given in class (check the values of R0 and V1 by DMM). The combination of the power
supply plus R0 plays the role of a battery with internal resistance (the internal resistance of the power
supply is negligible). Now vary the load resistance RL from 10 Ω to 1280 Ω, increasing the resistance
by a factor of two each time. For each value of RL, record the resulting values of I and VRL.
We are interested in the power dissipated by RL, as a function of RL; you now have the required data
to plot such a function (use your measured values of I and VRL to calculate the dissipated power, as
the nominal values of the decade resistance box are not to be trusted). Enter your values in Graphical
Analysis and plot the function of interest; you will increase the accuracy of your plot if you measure
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the values of RL with your DMM instead of using the values from the decade resistance box. From
your plot, read off the value of RL for which the dissipated power is a maximum and compare with
measured value of R0.
The power dissipated in the load resistor is given by following expression
?? = � ??1
??0 + ????
�
2
????
You have to show the derivation of this expression in your lab report. To explain your result, some
calculus is required. To find the value of the load resistance where the power dissipated is a
maximum take the derivative of PRL with respect to RL, set that derivative equal to zero, then solve
for RL. Show this work in your analysis.
To quantify the comparison from your plot, use the curve-fitting capability of Graphical Analysis.
Use the equation for PRL as a function of RL and fit your plot to this theoretical equation. Compare
the resulting constants with your measured values of R0 and V1 (again, measure V1 with your DVM
instead of trusting the power – supply meter). Report these comparisons in your conclusions.
Figure 2: Circuit for part 2.
Notes and Hints
1. Don’t forget to include your calculation of the value of RL that maximizes the power dissipated by
the load resistor.
2. Use your measured values of I and V to determine PRL for plotting versus RL. The curve fitting can
be done using ANALYZE/CURVE FIT in Graphical Analysis. For ease of inputting the function use
parameters A instead of ε and B instead of R0. Once you define the function you can check
“automatic” under fit type in the upper right corner. Graphical Analysis will then return the values
of A and B that provide the best fit to your data. These should match the values in your circuit. Do
they?
Self-assessment questions:
1. State Kirchhoff’s junction rule.
2. State Kirchhoff’s loop rule.
3. What is the unit of power?