Physics 261
Kirchhoff’s Laws in DC Circuits
Kirchhoff’s Laws apply conservation of energy and conservation of electric charge to DC circuits:
the sum of the potential energy differences across all elements of a closed circuit is zero (Kirchhoff’s
voltage or loop rule), and the sum of all currents entering a junction and the sum of all currents
leaving the junction are equal (Kirchhoff’s current or junction rule). If all resistor and emf values are
known, then the current through each resistor can be calculated because the specification of a complete set of independent equations satifying the loop and junction rules for any DC circuit includes
as many equations as there are unknown currents, and the equations may be solved simultaneously
for these currents in terms of the resistor and emf values.
You will perform such an analysis on the following circuit:
• Set up the system of equations based on applying Kirchhoff’s Laws to the circuit in the figure.
Use the element labels given in the figure, and solve for the five (5) currents in terms of these
labels, that is V1, V2, R1, R2, R3, R4, R5. All of this should be in your notebook when you
arrive to make the measurements.
• Determine the equation for the uncertainty in each of these prediction by performing error
propagation (using the method in your data analysis notes: partial derivatives) in terms of
these same variables. All of this should be in your notebook when you arrive to make the
measurements. [Since, as you should be able to see immediately, I1 = I2 , and I3 = I4 , this
isn’t quite as tedious as it might seem, but it will still take some work.]
• In the laboratory, select two (2) 100 Ω (nominal), two (2) 220 Ω (nominal), and one (1) 1 kΩ
(nominal) resistors; measure their resistances; using your specification tables, determine the
uncertainties of the resistances.
• With R1 = R4 = 100Ω, R2 = R5 = 220Ω, and R3 = 1 kΩ, plug the measured values (and
uncertainties, where necessary) into your previously determined current (and uncertainty)
equations and calculate predicted values for the currents.
• Assemble the circuit, with V1 = 10 V and V2 = 5 V, and, by inserting an ammeter into the
appropriate places in the circuit, measure the five (5) [actually, three (3) different] currents.
• Compare (quantitatively!) measurements and predictions.
• Are energy and charge conserved in your circuit?
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