Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

Mesh Current Analysis Circuit

Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE)

  •  One simple method of reducing the amount of math’s involved is to analyse the circuit using Kirchhoff’s Current Law equations to determine the currents, I1 and I2 flowing in the two resistors. Then there is no need to calculate the current I3 as its just the sum of I1 and I2. So Kirchhoff’s second voltage law simply becomes:
    Equation No 1 :    10 =  50I1 + 40I2
    Equation No 2 :    20 =  40I1 + 60I2
  • therefore, one line of math’s calculation have been saved.

Mesh Current Analysis

  • An easier method of solving the above circuit is by using Mesh Current Analysis or Loop Analysis which is also sometimes called Maxwell´s Circulating Currents method. Instead of labelling the branch currents we need to label each “closed loop” with a circulating current.
  • As a general rule of thumb, only label inside loops in a clockwise direction with circulating currents as the aim is to cover all the elements of the circuit at least once. Any required branch current may be found from the appropriate loop or mesh currents as before using Kirchhoff´s method.
    For example: :    i1 = I1 , i2 = -I2  and  I3 = I1 – I2
  • We now write Kirchhoff’s voltage law equation in the same way as before to solve them but the advantage of this method is that it ensures that the information obtained from the circuit equations is the minimum required to solve the circuit as the information is more general and can easily be put into a matrix form.
    For example, consider the circuit from the previous section.
    Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • These equations can be solved quite quickly by using a single mesh impedance matrix Z. Each element ON the principal diagonal will be “positive” and is the total impedance of each mesh. Where as, each element OFF the principal diagonal will either be “zero” or “negative” and represents the circuit element connecting all the appropriate meshes.
  • First we need to understand that when dealing with matrices, for the division of two matrices it is the same as multiplying one matrix by the inverse of the other as shown.
    Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE)
    Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE)
  • having found the inverse of R, as V/R is the same as V x R-1, we can now use it to find the two circulating currents.
    Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE)

  • Where:
    [V]   gives the total battery voltage for loop 1 and then loop 2
    [I]     states the names of the loop currents which we are trying to find
    [R]   is the resistance matrix
    [R-1 ]   is the inverse of the [ R ] matrix
  • and this gives I1 as -0.143 Amps and I2 as -0.429 Amps
    As : I3 = I1 – I2
  • The combined current of I3 is therefore given as :   -0.143 – (-0.429) = 0.286 Amps
  • This is the same value of  0.286 amps current, we found previously in the Kirchhoffs circuit law tutorial.

Summary

  • This “look-see” method of circuit analysis is probably the best of all the circuit analysis methods with the basic procedure for solving Mesh Current Analysis equations is as follows:
    • Label all the internal loops with circulating currents. (I1, I2, …IL etc)
    • Write the [ L x 1 ] column matrix [ V ] giving the sum of all voltage sources in each loop.
    • Write the [ L x L ] matrix, [ R ] for all the resistances in the circuit as follows:
       R11 = the total resistance in the first loop.
      Rnn = the total resistance in the Nth loop.
      RJK = the resistance which directly joins loop J to Loop K.
    • Write the matrix or vector equation [V]  =  [R] x [I] where [I] is the list of currents to be found.
The document Mesh Current Analysis | Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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FAQs on Mesh Current Analysis - Network Theory (Electric Circuits) - Electrical Engineering (EE)

1. What is mesh current analysis?
Ans. Mesh current analysis is a method used to analyze electrical circuits by applying Kirchhoff's voltage law (KVL) to determine the currents flowing in each closed loop, known as meshes, within the circuit.
2. How does mesh current analysis work?
Ans. In mesh current analysis, each mesh in a circuit is assigned a current variable. By applying KVL to each mesh, a system of equations is formed. These equations can then be solved simultaneously to find the unknown mesh currents and, subsequently, other circuit quantities.
3. Why is mesh current analysis used?
Ans. Mesh current analysis is used in electrical circuit analysis because it simplifies the process of solving complex circuits with multiple current sources and resistors. It provides a systematic approach to determine the currents flowing in different parts of the circuit.
4. What are the advantages of mesh current analysis?
Ans. The advantages of mesh current analysis include its ability to handle circuits with multiple loops, its systematic approach that reduces the chance of errors, and its efficient solution for finding mesh currents. It also helps in understanding the distribution of currents within a circuit.
5. Are there any limitations to mesh current analysis?
Ans. While mesh current analysis is a powerful tool, it does have some limitations. It is primarily applicable to circuits that can be represented by planar networks, meaning circuits that can be drawn on a flat surface without any overlapping branches. Additionally, it is not suitable for circuits with significant mutual inductance or capacitive coupling between components.
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