Kirchhoff's Rules

Lab #8

DC Circuits - Kirchhoff's Rules

Purpose:

The purpose of the lab is to study Kirchhoff's rules and apply them to complex DC circuits. These rules are then verified and Ohm’s Law is used for certain calculations.

Introduction Kirchhoff's rules are very useful in analyzing the currents and voltages in a circuit.

His rules state:

1. The sum of the currents entering a junction must be equal to the sum of the currents exiting that junction. The following formula is used: Σ Iin = Σ Iout.

2. The sum of the potential differences across each circuit element in a closed loop must be zero, in which Σ ∆V = 0.

Data

Voltage supply = 3.00 volts

Circuit I - Switch Closed

Resistor

R (Ohms)

V (Volts)

I (milliamps)

Power (Watt)

R1

76.5

2.00

20.1

0.0402

R2

13.4

0.240

23.1

0.0055

R3

51.2

1.778

34.9

0.0621

R4

22.7

0.249

10.9

0.0027

Rdecade

55.4

2.953

55.2

0.1690

*Sum of Currents at Each Junction

Junction

Current Sum (milliamps)

A

55.2

B

34.9

C

43.2

D

98.4

*Sum of Voltages Around Each Loop

Loop

Voltage Sum (volts)

1

.559

2

-0.092

3

0.062

4

.404

5

3.522

6

.496

7

.466

Circuit II - Switch Open

Resistors

R (Ohms)

V (Volts)

I (milliamps)

Power (Watt)

R1

76.5

1.41

14.2

0.0200

R2

12.4

0.146

14.0

0.0020

R3

50.9

1.578

31.0

0.0489

R4

22.7

1.000

44.1

0.0441

Rdecade

55.4

2.510

45.3

0.1137

*Sum of Currents at Each Junction

Junction

Current Sum (milliamps)

A

44.1

*Sum of Voltages Around Each Loop

Loop

Voltage Sum (volts)

1

3.088

2

3.066

3

0.022

Kirchhoff's Rules - Current through each Resistor

Measured Value of

Current (mA)

Calculated Value of

(Current (mA)

Percent

Error

I1 → RB

45.3

44.73

1.27%

I1 → R4

44.1

44.73

1.41%

I2 → R1

14.2

14.16

0.282%

I2 → R2

14.0

14.16

1.13%

I3 → R3

31.0

30.57

1.41%

Discussion/Conclusion: This experiment was intended to verify Kirchhoff's rules using DC circuits.

It was determined that there are 7 loops and 4 junctions in circuit I. There were 3 loops in circuit II and only one junction. our results are not very accurate and there are a variety of reasons why there are discrepancies with our experimental values and that which is expected based on Kirchhoff's rules. Many sources of error in this experiment may have affected the interpretation of the results. An important source of error is human error, such as inaccurate reading of the voltage and resistances in the experiment. Furthermore, there may be an error in miscalculation for the current and power in each of the parts of the experiment. Human error can be reduced in the experiment by one working slower, and being more cautious. Another important source of error is the equipment used during the experiment. Initially, the digital multimeter was not working properly and was reading the voltages incorrectly, so we had to change it to a different one. It is important to make sure that the equipment is set up correctly and that the power supply is calibrated correctly. The power supply and equipment should be checked and tested before starting the experiment in order to reduce sources of error.

Questions:

1. Do your measurements agree, within experimental errors, with Kirchhoff's rules? Discuss your results.

The measurements do agree within the experimental errors of Kirchhoff's rules. For the circuit with an open and closed switch, the sum of current at each junction was relatively close to the current that was measured during the experiment. For example, in the closed switch, the sum of the current at junction A was calculated to be 55.0 mA, but the measured value was 55.2 mA so these values differ by 0.2 milliamps. Junction B is equivalent to the current going through R3 which was calculated to be 34 amps and is relatively close to the measured value of 34.9 mA. Junction C is equal to the current going through R1 and R2, which was calculated to be 43.mA. Junction D is equivalent to the current going through R1, R2, and R4, which was calculated to be 98.1mA.

For the open switch, Junction A was