01 Maxwell Loop Current Theorem Verification

Exp:1 Title: verification of Maxwell loop current theorem. Theory: This method which is particularly well-suited to coupled circuit solutions employs a system of loop or mesh currents instead of branch currents (as in Kirchhoff’s laws). Here, the currents in different meshes are assigned continuous paths so that they do not split at a junction into branch currents. This method eliminates a great deal of tedious work involved in the branch-current method and is best suited when energy sources are voltage sources rather than current sources. Basically, this method consists of writing loop voltage equations by Kirchhoff's voltage law in terms of un-known loop currents. Circuit Diagram: We construct a circuit like Figure 1.1 . Apparatus required : (1) Bread Board (2) DC supply (3) Resistors (4) One Multi-meter (5) Wires Measurements: E 1 = 5 V, E 2 =6 V R1= 46.2 Ω R2= 23.2 Ω R3 = 39 Ω R4 = 33.4 Ω R5 = 33 Ω RL = 33.6 Ω OBSERVATION: I 1 =75.82 mA I 2 = 3.78 mA I 3 =-66.93 mA I BF = 72.08mA I CG =70.65mA Calculated value: According to the KVL, we can write the following equations, For loop1: -I 1 R 1 -(I 1 –I 2 )R 4 +E 1 =0 For loop2: -I 2 R 2 -(I 2 -I 3 )R 5 -(I 2 -I 1 )R 4 =0 For loop 3: -I 3 R 3 -E 2 -(I 3 -I 2 )R 5 =0 79.8I 1 -33.4I 2 =6 33.4I 1 -89.6I 2 +33I 3 =0 33I 2 -72I 3 =5 I 1 =76.71 mA I 2 =3.63 mA I 3 =-67.78 mA

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Electrical Engineering : Practical Purpose

Transcript of 01 Maxwell Loop Current Theorem Verification

Page 1: 01 Maxwell Loop Current Theorem Verification

Exp:1

Title: verification of Maxwell loop current theorem.

Theory: This method which is particularly well-suited to coupled circuit solutions employs a system of loop or mesh currents instead of branch currents (as in Kirchhoff’s laws). Here, the currents in different meshes are assigned continuous paths so that they do not split at a junction into branch currents. This method eliminates a great deal of tedious work involved in the branch-current method and is best suited when energy sources are voltage sources rather than current sources. Basically, this method consists of writing loop voltage equations by Kirchhoff's voltage law in terms of un-known loop currents.

Circuit Diagram: We construct a circuit like Figure 1.1 .

Apparatus required : (1) Bread Board (2) DC supply (3) Resistors (4) One Multi-meter (5) Wires

Measurements: E 1= 5 V, E2 =6 V

R1= 46.2 Ω R2= 23.2 Ω R3 = 39 Ω R4 = 33.4 Ω R5 = 33 Ω

RL = 33.6 Ω

OBSERVATION: I1 =75.82 mA I2= 3.78 mA I3=-66.93 mA IBF= 72.08mA ICG=70.65mA

Calculated value:

According to the KVL, we can write the following equations,

For loop1: -I1 R1 -(I1 –I2 )R4 +E1 =0

For loop2: -I2R2-(I2-I3)R5-(I2-I1)R4=0

For loop 3: -I3R3-E2-(I3-I2)R5=0

79.8I1-33.4I2=6

33.4I1-89.6I2+33I3=0

33I2-72I3=5

I1=76.71 mA I2=3.63 mA I3=-67.78 mA

IBF= I1- I2=73.08 mA

ICG=I2-I3=71.41 mA

Page 2: 01 Maxwell Loop Current Theorem Verification

CAUSES OF ERROR : . The differences in the result are due to the tolerance of the resistors and human error in reading the multi meter. Heating of the resistors could have also caused some error but unlikely due to the low level of power used.

CONCLUSION: As the figures under the column percentage of error are small, we can say Maxwell loop current theorem holds good .

Observed value

Calculated value (mA)

Percentage error

I1 75.82 76.71 1.16I2 3.78 3.63 4.13I3 -66.93 -67.78 1.25IBF 72.08 73.08 1.36ICG 70.65 71.41 1.06