Physics 220 General Physics II Grist Laboratory Exercise: Kirchhoff’s Rules Object Through experiment you will determine if the currents and voltage drops in a two loop circuit obey Kirchhoff’s rules. Introduction A two loop circuit is a circuit that has two distinct, yet interconnected, current paths through which current may flow. You will be measuring the currents and voltage drops in a two loop circuit with multiple resistors and emf sources and comparing your measurements to calculated values. What are Kirchhoff’s rules? 1) The Junction Rule. This states that when you have a point where two or more wires connect (a junction) the sum of the currents going in to the junction must be equal to the sum of the currents leaving the junction. This makes sense if you consider the law of conservation of charge – you can’t suddenly gain (or lose) charges from nowhere just by entering or exiting a junction. 2) The Loop Rule. This states that the sum of all the voltage drops and emf sources around a loop must equal zero. This make sense if you consider that the emf (voltage) provided is distributed over the resistances in the loop – you can’t ‘magically’ have voltage that isn’t provided by some emf source. Kirchhoff’s Rules 1 Physics 220 General Physics II Grist The Two Loop Circuit I1 I2 R2 R5 R3 I3 loop 2 loop 1 E1 R1 E2 R4 Figure 1 By applying Kirchhoff’s rules to the two loop circuit in Figure 1, we get the following equations: (1) (2) E1 V2 V3 V1 0 E1 R2 I1 R3 I 3 R1 I1 0 E2 V4 V3 V2 0 [Loop 1] [Loop 2] E2 R4 I 2 R3 I 3 R5 I 2 0 (3) I 3 I 2 I1 [Junction] If we know the resistances and the emf values, then we have three equations with three unknown values (I1, I2, and I3). We can now use any one of several method of solving simultaneous linear equations and find the unknowns. Procedure 1. Arrange the circuit shown in Figure 1 using first set of resistors. 2. Adjust the two power supplies: E1 to 10 V dc and E2 to 5 V dc. 3. Using the ammeter function on the multimeter measure the current I1 through R2 and record on the report sheet. 4. Now measure the current I2 through R5 and record on the report sheet. 5. Measure the current I3 through R3 and record on the report sheet. 6. Also measure the currents through R1 and R4 and record on the report sheet. 7. Now using the voltage function on the multimeter measure and record the voltage drop across each resistor. 8. Now using the ohmmeter function on the multimeter carefully remove, measure and record the resistance of each resistor. Now repeat with the second set of resistors Kirchhoff’s Rules 2 Physics 220 General Physics II Grist Comparison and Analysis 1) Using equations (1), (2), and (3) in the RnIn form, and the measured values of the power supplies and the resistors, solve for the three currents. Compare to the measured values of the currents. Do the measured and calculated values agree closely enough to validate Kirchhoff’s rules? 2) Using your measured values for the currents does I 3 I 2 I1 within reason enough to validate Kirchhoff’s junction rule? Show and comment. 3) Using your measured values, do the loop equations (1) and (2) agree closely enough to validate Kirchhoff’s loop rule? Show and comment. 4) Why are the voltages with the two sets of resistors the same, while the currents are different? Kirchhoff’s Rules 3 Physics 220 General Physics II Grist Name_____________________________ DATA SHEET Resistor Set 1 Measured E1 E2 I1 I2 I3 IR1 IR2 ΔV1 ΔV2 ΔV3 ΔV4 ΔV5 R1 R2 R3 R4 R5 Calculated Resistor Set 2 Measured Calculated E1 E2 I1 I2 I3 IR1 IR2 ΔV1 ΔV2 ΔV3 ΔV4 ΔV5 R1 R2 R3 R4 R5 Kirchhoff’s Rules 4