Lab Report

1

4

University

DC Circuits Laboratory EET 104EA

Workbook Lab #4

Kirchhoff’s Current Law

Student’s name

Partner’s name

Instructure’s name

Sep, 17 2015

INTRODUCTION

This experiment involved verification and applying of Kirchhoff’s Current Law (KCL) in single-node-pair circuits. According to Kirchhoff’s current Law (KCL), at any junction point in the circuit, the summation of all the branch currents should be zero. The law is imperative in analysis of electrical networks and therefore the experiment aimed at verifying and illustrating how the law applies.

LIST OF EQUIPMENTS AND COMPONENTS

Instruments:

· Fluke model 189

· Handheld digital multimeter

· K & H model IDL – 600

· Analog lab

Components:

· (1) each: 2.2kΩ, 3.6kΩ, 4.3kΩ, 10kΩ

· ¼ - watt resistors; other values as needed

Other:

· 24-gauge solid jumper wires

PROCEDURE

1) Measure and record the exact vales of the 2.2kΩ, 3.6kΩ, and 4.3kΩ resistors. Calculate and record their conductances.

2) Construct the circuit as shown below, on the analog lab’s breadboard. The 10 V source together with the 10kΩ resistor approximate an ideal current source.

3. Apply power to the lab, measure and record the voltage across each branch of the circuit using the reference direction shown.

4. Using the results obtained above, determine whether Kirchoff’s current law is satisfied for this circuit.

RESULTS AND CALCULATIONS

B. Verifying Kirchhoff’s Current Law

Step 1

Exact vales of

2.2kΩ ≈ 2.1737kΩ

3.6kΩ ≈ 3.5641kΩ

4.3kΩ ≈ 4.2578kΩ

10kΩ ≈ 9.8640kΩ

10V ≈ 10.047V

I1 ≈ 0.919mA

I2 ≈ 0.432mA

I3 ≈ 0.263mA

I4 ≈ 0.221mA

According to Kirchhoff’s current Law, at any junction point in the circuit, the summation of all the branch currents should be zero.

0.002 is approximately equal to zero. The small discrepancy can be attributed to errors in measurements and resistance of the connecting wires which was not taken into consideration.

Thus, the results are in accordance with the Kirchhoff’s current Law.

C. ANALYZING A SINGLE-LOOP CIRCUIT

1.

2.

By applying Kirchoff’s current law and Ohm’s law, the expected value of can be calculated as follows

3.

The values of in both the cases are approximately the same. The small discrepancy can be attributed to errors in measurements and resistance of the connecting wires which was not taken into consideration.

4.

5.

The result of the summation of inductances (1.0768kS) is approximately equal to the calculated value (1.025kS).

The overall conductance of several resistors connected in parallel is equal to the sum of the conductance of each resistor.

D. DESIGNING A MILLIAMMETER

1.

Rm = 1.7872kΩ

Current indicated by microammeter =

2.

When the microammeter full-scale current reading is,

Using Ohm’s law, V=IR

3.

The required value of the shunt resistor for desire full-scale current of 1mA

4. Testing the milleammeter design

Variable Supply (mA)	Actual current flow indicated on digital multimeter (µA)	Actual current through milliammeter (µA) Reading
0.1	8	80
0.201	17	170
0.308	27	270
0.401	35	250
0.507	44	440
0.603	53	530
0.699	62	620
0.802	72	720
0.899	80	800
1.003	90	900

CONCLUSION

The experiment has verified the Kirchhoff’s Current Law (KCL), which states that at any junction point in an electrical circuit, the summation of all the branch currents is equal to zero. The Kirchhoff’s Current Law is critical in circuit analysis. It is used in circuit analysis with the combination with the Kirchhoff’s Voltage Law and the Ohm’s law. The experiment also showed that the Kirchhoff’s Current Law can be used in analytical calculations to make predictions of experimental values. The errors obtained between the calculated and experimental values were insignificant proving the correctness of the Kirchhoff’s Current Law. Thus, Kirchhoff’s laws are valid as proved by the experiment. The experiment was also used in testing a milliammeter design where it was shown that while making readings on older analog-style meters, the scale factor has to be accounted for.