Date Course Name Instructor Name Student(s) Name MULTILOOP CIRCUIT When a general circuit cannot be analyzed directly by using Ohm’s law, it can be analyzed by using Kirchhoff’s rules. To understand Kirchhoff’s rules, one should have a clear understanding on some terms: (a) junction is a point in a circuit where three or more connecting wires meet; (b) branch is a path connecting two junctions; and (c) loop is a closed path of two or more branches. Kirchhoff’s rules embody two basic conservation laws. First law or the junction rule is basically the conservation of charges, which states that the algebraic sum of the currents at any junction is zero. I=0 Second law or the loop rule is basically the conservation of energy, which states that the algebraic sum of the voltage changes around a closed loop is zero. V = 0 STUDENT OUTCOMES Through this experiment, students will learn: - distinguish between circuit branches and junctions - how to use Kirchhoff’s rules to multiloop circuits - explain how Kirchhoff’s rules are related to conservation of charge and energy - how to determine resistance values using the color code MATERIALS Tablet PC Computer Laptop Logger Pro Vernier Current Probe Vernier Differential Voltage Probe Vernier Computer Interface Circuit Board Two Power Supplies Wires PRELIMINARY QUESTIONS: 1. Do Kirchhoff’s rules represent any new physical principles like Ohm’s law does? Explain 2. What is a junction. In the first circuit given below, where are the junctions? 3. Distinguish between a branch and a loop. In the first circuit below, what are the branches? the loops? PROCEDURE: 1. Examine the resistors. The color bands on the resistors conform to a color code that gives the resistance value. Look up the color code and identify the value of the resistors given. Also, the resistance value may vary depending on the tolerance as indicated by the last band (gold +/- 5%, silver +/- 10%, no band +/- 20%) 2. Connect the two loop circuit. The power supplies must be set to the given values before connecting the circuit. Do not turn on the circuit until after it has been checked by the instructor/peer mentor. 3. Connect the current and voltage probes to the logger pro. Be sure to calibrate the probes to zero as you did in the previous exercises. 4. After the circuit has been checked, turn on the power supplies and measure the “operating” value of each battery using the voltage probe. Record the values on the table. 5. Temporarily open the switches and insert the current probe in series with one of the branches. Close the switch and record the branch current. 6. Repeat step 5 for all the branches. 7. Connect the three loop circuit below. Repeat steps 4 – 6 for this circuit. DATA TABLE 1: R1 = _________ R2 = _________ R3 = _________ Measured value V ( Volts) Theoretical value I (Ampere) Percent Error V1 V2 I1 I2 I3 DATA TABLE 2: R1 = ________ R4 = _________ R2 = _________ R5 = _________ R3 = _________ Measured value V ( Volts) V1 V2 I1 I2 I3 I4 I5 Theoretical value I (Ampere) Percent Error ANALYSIS: 1. Label the directions of your current for analysis. 2. Choose the direction you will be taking in going around the loop. 3. Using the junction rule, write the equation for each junction in the loop. Remember, that for each circuit, you will get n – 1 independent equations when using the junction rule. 4. Using the loop rule, write the equation for each loop. use the measured “operating” values for V1 and V2. Remember that if you have n unknowns, you should also have n independent equations to work out the problem. 5. Using the equations from the junction and loop rules, solve for the currents. 6. Compare the theoretical values for the current (from calculations) with the measured values by finding the percent error. 7. Show all calculations. 8. Using the data in Table 1, calculate the power output of the batteries and the power input to the resistors. QUESTIONS: 1. Compare the power supplied by the batteries to that dissipated by the resistors. What would you expect, and what principle does this illustrate. 2. The Wheatstone bridge circuit had several loops. (a) When the bridge was balanced, are Kirchhoff’s rules needed to calculate the currents through the resistors? Why? Could Kirchhoff’s rules be used? (b) If the bridge was not balanced, are Kirchhoff’s rules needed? Explain. 3. Draw a diagram showing the junctions and loops of an unbalanced Wheatstone bridge. How many simultaneous equations would be needed to analyze the circuit? 4. Two batteries with emf of 1.5 V and 1.2 V and internal resistance of 0.5 and 0.8 respectively, and connected in parallel with + terminals together. (a) Find the current the in an external 2 resistor. (b) Would more current be delivered if only one battery was used? If so, which one? Explain.