Ch20_Kirchoff+Lab

Purpose:

To determine how currents split in multiple loops

Hypothesis:

When current approaches a junction, it will split, but not always evenly. Most of the current will take the path of least resistance.

Set Up:
 * Procedure:**

Circuit A

Circuit B

Circuit C

Circuit D

1. Set up the 4 circuits as shown above. 2. Draw the schematic diagram for each circuit. 3. Measure the current and voltage in every resistor. Make sure to measure the voltage and current through the batteries and power supplies as well. 4. Calculate theoretical current and voltage. 5. Calculate Percent Error.

Materials:

Resistors, wire leads, batteries, multimeter, power supplies, wires.


 * Data:**




 * Calculations**

Circuit A



I1 = I2 + I3 I3 = I4 + I5 I2 = -I5 + I6 0 = 6 - I2*560 - I6*100 0 = 6 - I3*100 - I4*300 0 = 6 - I3*100 - I5*300 - I6*100

Matrix

1-1-1+0+0+0=0 1+0+0-1-1+0=0 0+1+0+0+1-1=0 0+560+0+0+0+100=6 0+0+100+300+0+0=6 0+0+100+0+300+100=6

I1=24mA I2=7.7mA I3=16mA I4=14mA I5=9.1mA I6=.017mA

Circuit B



I1 = I2 + I3 0 = -5 - I1*750 - I2*500 + 10 0 = -5 - I1*750 - I3*1000

Matrix

1-1-1=0 -750-500+0=5 -750+0-1000=5

I1 = 1.54mA I2 = 6.15mA I3 = 7.69mA

Circuit C



I1=I2+I3 I3=I5+I4 0=10-I1*1000-I2*820 0=10-I1*1000-I5*680+5 0=10-I1*1000-I4*560

Matrix

1-1-1+0+0=0 0+0+1-1-1=0 1000+820+0+0+0=10 1000+0+0+0+680=15 1000+0+0+560+0=10

I1=9.51mA I2=.589mA I3=8.93mA I4=.863mA I5=8.06mA

Circuit D



I1=I2+I3 0=5.25-I2*200+1.56-I1*100 0=5.25+1.63-I3*475

Matrix

1-1-1=0 100+200+0=6.81 0+0+475=6.88

I1 = 28mA I2 = 15.8mA I3 = 12.6mA

__Miscellaneous Calculations__

Percent Error (Current) = |Theoretical - Experimental|/Theoretical *100 Percent Error = |1.54- 1.45|/1.54 *100 Percent Error = 5.84%


 * Discussion Questions:**

1. Are the experimental values of the currents for the entire laboratory generally larger or smaller than the theoretical values expected for the currents?
 * The experimental values of the currents are generally larger. For the most part they are around the same.

2. It was pointed out in the laboratory that some error might be caused by neglect of the internal resistance of the //emf//. Would the internal resistance cause an error in the direction shown in your answer to question 1? State your reasoning for the direction of any error caused by the internal resistance.
 * No. The internal resistance would increase overall resistance in the circuit. This was taken into account in my calculations, which is why the theoretical values are slightly lower, as current would be smaller with a greater resistance.

3. An ideal ammeter has zero resistance. Real ammeters have small but finite resistance. Would ammeter resistance cause an error in the proper direction to account for the direction of your error indicated in question 1? State your reasoning.
 * No because the resistance in the ammeter would lower the current. Ammeter resistance should lower the experimental values; mine were still higher than the theoretical.

4. The connecting wires in the experiment are assumed to have no resistance, but in fact have a finite resistance. Would this error be in the proper direction to account for the direction of the error stated in your answer to question 1? State your reasoning.
 * No. For the same reason as #3, the added resistance should lower values. My values were still higher than the theoretical values.

5. What is the meaning of any current values obtained in your solutions that are negative?


 * Negative current values are obtained when during drawing of current direction, the current drawn is opposite of what it actually is.


 * Conclusion:**

My hypothesis was correct and my data supports this. When current reached a junction, it split, and the majority of the current took the path of least resistance. In my results for Circuit A, the highest current was traveling through the resistor with the least resistance, the 100 ohm resistance - 20.9 milli amps of current were traveling through it. The same can be seen in Circuit B. The smallest resistor, 500 ohms, had the most current flowing through it - 7.68 milli amps.

In some of my circuits I had very small error, while in others I had larger error. Some sources of error could be the multimeter itself. It doesn't give consistent readings, as the numbers on the screen jump around a lot, so I am forced to "guess" the best estimate from the numbers on the screen. Also, the multimeters aren't consistent with other multimeters. I could get a reading, say 5.2 volts across a battery, and another person with a different meter could get a reading of 4.8 volts. That is a very big difference and could account for varying degrees of error between lab reports. Another source of error could be the resistances not taken into account, such as the resistance in the wires, multimeter, and internal resistance of the battery. These values would affect the overall readings and calculations.

To improve the error, I would get much better multimeters; ones that were consistent with each other and ones that gave accurate and precise readings. Me having to "guess" what the meter read definitely affected my results. I could apply the knowledge gained from this lab if ever I need to do any electrical work around the house. For example, if I need one appliance to receive more current, I would make sure it had the path to it had less resistance than other paths.