Download Measurement Lab

Physics 102
Kirchoff’s Law
February 14, 2006
Eduardo Nunez, Joseph Lan
Abstract:
The purpose of this lab is to apply Kirchoff’s Law to multi-loop circuits as well as
measuring branch currents with predicted currents.
Equipment:

Breadboard

Resistors

VOM

Old Fashion Ammeter (Analog)

3 Power Supplies

Wires
Procedure:
1. Collect all the equipment.
2. Set up circuit 1.
3. Record resistor values.
4. Measure the voltage across each resistor.
5. Record values.
6. Measure the current across each branch.
7. Set up equations for calculations.
8. Record values.
9. Set up circuit 2.
10. Record resistor values.
11. Measure the voltage across each resistor.
12. Record values.
13. Measure the current across each branch.
14. Set up equations for calculations.
15. Record values.
Calculations: (see also excel sheet)
Circuit 1 (assuming current flows clockwise both sides)
R1 = 180 Ω
V1 = 6V
R2 = 820 Ω
V2 = 3V
R3 = 560 Ω
V3 = 9V
Current through R1 = I1
Current through R2 = I2
Current through R3 = I3
1. I1R1 + I2R2 = V1 – V2 – V3
2. V3 + V2 = I3R3 – I2R2
3. I1 = I2 + I3
1. 180Ω I1 + 820Ω I2 + 0Ω I3= - 6V
2. 0Ω I1 – 820Ω I2 + 560Ω I3 = 12V
3. I1 - I2 - I3 = 0
Using matrices…
180
820
0
-820
1
-1
=
0
560
-1
-1
-6
12
0
.0022
-.0078
.0100
This means that current I1 is 2.2mA, current I2 is 7.8mA (but in the wrong direction
of which we chose), and current I3 is 10mA.
Circuit 2 (assume current flows clockwise)
R1 = 180 Ω
V1 = 6V
R2 = 120 Ω
V2 = 3V
R3 = 560 Ω
V3 = 9V
R4 = 820 Ω
a. I1R1 - I1R4 = 6V
- (R1 + R4) I1 = 6
-1000 I1 = 6
I1= -.006
b. I1 = I2 + I3
-.006 = I2 + I3
-.006 - I2 = I3
c. I2 = 0, because there is no voltage attached to them and they are “floating resistors”
then…
-.006 - 0 = I3
-.006 = I3



I1= -.006 units!!!!
I2 = 0
I3 = -.006
Error Analysis:
There are many possible sources of error and here is only a small list of some:
 The wires have some resistance which we assume non-existent for this experiment,
will affect slightly the measurement of the current.
 The resistors are not their stated Ohms because it has degraded.
 The VOM was incorrectly calibrated or just inaccurate.
 The VOM was connected in the wrong place therefore a wrong reading.
 The old fashion ammeter was not calibrated correctly or just inaccurate
 The old fashion ammeter may have been connected in the wrong place.
Percent Error: (for rest of percent error, see excel sheet)
% error = (theoretical – experimental)/theoretical x 100%
Example: Current I1
((2.2 – 2.2)/2.2 )*100% = 0%
Conclusion:
We have found the currents to be as listed above. For circuit one, we found out that
the current does flow in a clockwise direction all around, but that the current for the
R2 is in the opposite direction. For circuit two, we found that the current flows in a
counterclockwise direction and not a clockwise direction, as we had assumed. We
found out also that in a floating branch like in circuit two, the voltage and current
running through is going to be zero. All in all, we find Kirchoff’s Law to be very
interesting.
Grade: 98/100