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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.