Experiment 17: Kirchhoff’s Laws for Circuits

1 Experiment 17: Kirchhoff s Laws forCircuitsFigure : Kirchhoff s Law circuit BoardFigure : Schematic for Kirchhoff s CircuitEQUIPMENT(1) Universal circuit Board(2) D-Cell Batteries ( V)(2) Battery Holders(4) Alligator Clips(1) DMM(5) Resistors:R1= 10 ResistorR2= 12 ResistorR3= 15 ResistorR4= 18 ResistorR5= 22 Resistor8990 Experiment 17: Kirchhoff s Laws for CircuitsAdvance ReadingText:Kirchhoff s Voltage Law, Kirchhoff s CurrentLawLab Manual: Appendix A: Math Review(solving 3equations with 3 unknowns)ObjectiveThe objective of this Experiment is to apply Kirchhoff srules for Circuits to a two-loop circuit to determine thethree currents in the circuit and the electric potentialdifferences around each two basic laws of electricity that are most usefulin analyzing Circuits are Kirchhoff s laws for currentand s Current Law(The Junction Rule) statesthat at any junction (node)

2 Of a circuit , the algebraicsum of all the currents is zero (sum of the currentsentering the junction equals the sum of the currentsleaving the junction). In other words, electric chargeis conserved. Iin= Iout( )Kirchhoff s Voltage Law(The Loop Rule) states thataround any closed loop or path in a circuit , the alge-braic sum of all electric potential differences is equalto zero. Vi= 0( )To calculate magnitudes of current and voltage in acircuit like Fig. , you will need to write three equa-tions, making use of both the loop and junction results in three equations with three this Experiment , you will measure iandRi, thensolve for the three currents, might be able to guess the direction of currentflow in a circuit , given a circuit such as the one in thisexperiment.

3 However, as long as the current directionchosen at the beginning is used consistently through-out the calculation, the calculation will be correct. Forthe purposes of this Experiment , all currents will be as-sumed to be in the direction shown in Fig If anycurrent is measured or calculated to be negative, thatcurrent actually flows in the opposite direction of whatis indicated in Fig the following rules when writing a KVL equa-tion for a loop: If a source ofemfis traversed from to +, thechange in potential is + ; if it is traversed from+ to , the change in potential is.

4 Current flows from high potential to low poten-tial. A loop crossing a resistor with the currentconstitutes a negative potential difference. Aloop crossing a resistor against the current yieldsa positive potential : Potential Difference Sign ConventionWrite and equation relating the currents to each otherusing the junction rule,. Then write equations for twodifferent loops in terms of electric potential example, the equation for the currents in the topcenter junction in Fig :i1=i2+i3( )And an equation for the loop consisting of 1, R1, R2, andR3in Fig is: 1 R1i1 R2i3 R3i1= 0( )Write a similar equation for the loop consisting of 2, R4, R5, andR2, then solve this system of three equa-tions for the currents we predict through the three 17: Kirchhoff s Laws for Circuits91 Name:1.

5 Write the equation, then briefly explain: (20 pts ea.)(a) Kirchhoff s Voltage Law (KVL)(b) Kirchhoff s Current Law (KCL)2. Consider the circuit shown in Fig. and theEquipmentlist on Page 89. Use Kirchhoff s Current Law andVoltage Law to solve for the theoretical currents,i1, i2, performing the Experiment , measured values will be used for the emfs and resistances. For the pre-lab, use thenominal values as stated in theEquipmentlist.(a) Write the system of three equations. (30 pts)(b) Solve forI1,I2, andI3using substitution. (30 pts)92 Experiment 17: Kirchhoff s Laws for CircuitsPROCEDUREPART 1: Loop Method - Calculations1.

6 Determine the nominal resistance and tolerance ofeach resistor by reading its color code (Table ,Page 78). They should have the following approxi-mate resistances:R1= 10 R2= 12 R3= 15 R4= 18 R5= 22 2. Measure the resistance of each resistor using Construct the circuit shown in Fig. Do notconnect the Measure of the two batteries using a should each be at least V. Turn off theDMM and disconnect the batteries so they do Using your knowledge of the loop and junction rules,write three equations relating].6. Solve these equations by substitution to find thetheoretical currents.

7 A negative value simply indi-cates the current flows in the other 2: Current & Voltage Laws Applied7. Connect the batteries to the Measure the current in each of the three branches ofthe circuit . Refer to Fig. for proper ammeterconnection technique. Disconnect the batteries andturn off the DMM after Compare the measured values of current with thecalculated values. If they are not approximatelyequal, check your calculations or retest the Reconnect the batteries and measure the electricpotential across each element of the circuit . Signand direction are crucial; measure based on the hy-pothetical directions of current you chose at the be-ginning.

8 This means the black lead will be placedwhere current enters the resistor and the red leadwill be placed where current leaves the : Ammeter ConnectionPART 3: Non-Ideal VoltmeterAt the front of the room, your TA has set up twoseries Circuits . One circuit has two 100 resistors,the other circuit has two M resistors. Takeyour voltmeter to this table. Adjust the power sup-ply on each circuit to Measure the potential differences across each of theresistors in the 100 circuit . Is the magnitude oftheir sum equal to the potential difference acrossthe power supply? Show Measure the potential difference across each of theresistors in the M circuit .

9 Is the magnitudeof their sum equal to the potential difference acrossthe power supply? Show 17: Kirchhoff s Laws for Circuits93 QUESTIONS1. Explain what effect the DMM will have on the cir-cuit when inserted to measure Do the values fromPart 2verify Kirchhoff s Cur-rent Law?3. Do the values fromPart 2verify Kirchhoff s VoltageLaw?4. Would disconnecting the emf source on the left loopof the circuit , 1, affect the currentI2? CalculatewhatI2is for this case. What A voltmeter is connected in parallel to a resistorwhen measuringVi. Remember that the internalresistance of the DMM, when used as a voltmeter,is approximately 10 M.

10 CalculateReqof the volt-meter connected to a resistor in each circuit ofPart Use the above information to discuss why the volt-age measured across the 10 M resistors did notequal the voltage measured across the power sup-ply.