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Electrical Principles - Chapter 5: Kirchhoff's Current and Voltage LawsPublish Date: Mar 27, 2013 | 0 Ratings | out of 50.00

Overview

The Electrical Principles/Fundamentals series present the basic theories and concepts taught at entry level electronics courses at both 2 year and 4 year institutions. This series of content providesexamples to professors to enable them to easily teach concepts to students, who can develop a solid underlying knowledge of electronics using the NI solution. This series focuses on some of thebasic theory as well as providing the NI Multisim circuits to enable practical implementation end experimentation as homework for students.

Table of ContentsIn this Chapter

Example Courses

Kirchhoffs Current Law (KCL)

Kirchhoffs Voltage Law (KVL)

Example Problem

Suggested NI Solution

References

1. In this Chapter

We begin this chapter by exploring a couple of the basic rules of circuit analysis: Kirchhoffs Current and Voltage Laws. We will use the NI Multisim circuit teaching environment to verify our calculated results with example circuits that can be used by any educator or student.

If you do not have NI Multisim installed on your computer, you can download a free 30 day evaluation at http://www.ni.com/multisim/try/

2. Example Courses

Listed below are example courses that teach this concept at their schools.

Course Name School Learn More

Electrical Principles Conestoga College http://www.conestogac.on.ca/fulltime/0071.jsp

Electronic Technology 1 Macomb Community College http: //www.macomb.edu/noncms/Search/Courses/coursekey.asp?coursekey=ELEC-1161)

3. Kirchhoffs Current Law (KCL)

Kirchhoffs Current Law (Kirchhoffs First Law) states that the current entering a point in a circuit is equal to the summation of the currents exiting [1].

4. Kirchhoffs Voltage Law (KVL)

Kirchhoffs Voltage Law (Kirchhoffs second law) states that the summation of all voltage drops in a closed loop must equal to zero which is a result of the electrostatic field being conservative [2].

5. Example Problem

Let us now examine the below circuit and apply Kirchhoffs Laws to determine th e currents and voltage drops the n use NI Multisim to verify our calculated values.

STEP 1: Open circuit file kirchhoff_example.ms12. You will notice the circuit below [3].

Answer Sub-Step 1: Determine the currents I and I passing through each resistor.1 2

To apply KCL, begin by labelling the junctions in our circuit, and . Then we label the currents as , and in an arbitrary direction as shown in the figure below. (Direction of currents will beJ 1 J 2 I I1 I2confirmed once we complete the problem).

http://www.ni.com/multisim/try/http://www.ni.com/http://www.ni.com/multisim/try/

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Junction J : 1

(equation 1)I = I + I1 2

Junction J : 2

(which is the exact same equation we got from above)I + I = I1 2 J 1

Answer Sub-Step 2: Determine the voltage drops V and V across each resistor.R1 R2

Begin by labelling the loops as loop and loop as shown below.A B

(start from the upper left corner and move clockwise)Loop A :

-I x (100 ) + 1.5V = 0 (equation 2)1

Therefore: I = 0.015 A1

Loop B:

-9V I x (200 ) + I x (100 ) = 0 (equation 3)2 1

Substituting the value of I into equation 3 yields:1

-9 I x (200 ) + (0.015)(100 ) = 02

-7.5 = (200) x I therefore:2 I = -0.0375 A2

And then I = -0.0225 A

Note that the negative sign of the current indicates that the arbitrary direction we chose is the opposite of the actual direction the current is flowing in.

Answer Sub-Step 3: Determine the values of V and V based on our calculated values for I and IR1 R2 1 2

V = I x RR1 1 1 = (0.015 A) x (100 ) therefore V = 1.5VR1

V = I x RR2 2 2 = (-0.0375 A) x (200 ) therefore V = -7.5VR2

STEP 2: Open circuit file kirchhoff_example_current.ms12 using NI Multisim then open each individual multimeter by dou ble-clicking on each device and choosing the A button to measure thecurrent. Then, simulate the circuit by clicking on the run button or choosing Simulation>>Run Simulation.

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