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NIU PHYS 375 - Kirchoff’s Laws

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OverviewBackground1. Ohm’s Law2. Kirchoff’s Laws3. Thevenin’s TheoremPhysics 375, Laboratory 1Kirchoff’s LawsOverviewThe purpose of this experiment is to review the properties of resistors and batteries and to usethem to investigate Ohm’s law, Kirchoff’s laws and Thevenin’s theorem.BackgroundKirchoff’s laws are an application of the conservation of charge and conservation of energy toelectric circuits. The Kirchoff current law states that conservation of charge requires the sum ofall current into and out of a point in a circuit must equal zero. The Kirchoff voltage law states thatconservation of energy requires the sum of all voltage drops around a closed loop of a circuit mustequal zero. Ohm’s law describes the relation between energy lost by electrical charges as theypass through resistive circuit elements, and that relation is a constant V=IR. Thevenin’s theoremtakes the fact that Kirchoff’s and Ohm’s laws are all linear relations between voltage and currentto prove that any network of batteries and resistors can be replaced by a single battery and resistorin series.1. Ohm’s LawConnect the variable power supply, digital multimeter (DMM), and a resistor in a circuit:Figure 1: Circuit for V-I measurementsSet the DMM to measure DC current in mA. The power supply has a built-in voltmeter to mea-sure DC volts. Use a 1 kΩ resistor for RL. Measure the current for each of the following voltages:0.2, 0.5, 1.0, 2.0, 5.0 V, and place them in a table. Use the values in the table to make a V-I graphfor the resistor.Repeat the above procedure replacing the resistor with a lamp. At what voltage does the filamentstart to glow? When does Ohm’s Law fail for a lamp?Now replace the lamp with a 1.5 V household battery, aligned with the positive connected to thepower supply positive, and switch the DMM to measure DC current in A. Repeat the procedure,but start at the minimum available for the circuit and go in steps up to 5 V. Does the battery obeyOhm’s Law?PowerResistor: RLDMMSupply: V+−PHYS375Lab1,p.22. Kirchoff’s LawsBuild the following circuit using the variable DC supply and three resistors:Figure 2: Resistor divider circuitMeasure the current through and the voltage across each of the three resistors (I1,I2,IL,V1,V2,VL). Write down the Kirchoff current law for each of the two junctions and compare to the mea-sured currents. Write down the Kirchoff voltage law for two loops of the circuit and compareeach equation to the measured values. Do they agree within measurement error?3. Thevenin’s TheoremRemove the load resistor RLfrom the preceding circuit to form a simple resistor divider. Firstmeasure the open circuit voltage, then measure the short circuit current. What is the equivalentvoltage and resistance?Set the variable supply to the equivalent voltage, and get a resistor (or two in series) equal to theequivalent resistance. Connect the power supply and resistor in series with the load resistor RL.Measure the current through RLand voltage across RL. Do they agree with the values measuredin the Kirchoff’s law measurement?Replace the power supply and resistors with the 1.5 V household battery and a 10 Ω resistor inseries. Measure the resistor’s resistance with the DMM. Measure the Thevenin equivalent circuitfor the battery and resistor by measuring the open circuit voltage and closed circuit current. Findthe equivalent resistance in the battery by subtracting the resistance measured for the resistor.Set the variable power supply to 1.000 V as measured by the DMM with a 1 M Ω resistance forthe load. Replace the load with a 100 Ω resistor and measure the voltage with the DMM. Keep inmind that the variable power supply can also be treated as an equivalent circuit. Measure theresistance of both resistors with the DMM and without measuring the closed circuit current, usethe two voltage measurements to estimate the equivalent resistance of the power


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NIU PHYS 375 - Kirchoff’s Laws

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