Question

Learning Goal: To use the mesh-current method to solve circuits containing resistors and both independent and dependent sources. The mesh-current method is a general technique for solving planar circuits. When the circuit contains a dependent source, that source will create a constraint and add an unknown to your system of equations. You must write a constraint equation for each dependent source, in addition to the KVL equations. Before beginning this tutorial, you should review the mesh-current method and the four different types of dependent sources. Part A - Find the meshes How many meshes does this circuit have? 12.5 k 2 10 kΩ 1 50 V 50 kΩΣ 75,000 ing

Answer 1

Number of meshes in the given circuit is two with the currents i1 and i2 flowing in their respective meshes. In an electrical circuit a mesh is nothing but a loop with electrical elements where the loop starts and end at same point.

Number of meshes = 2

The equation of the mesh currents of the mesh with i₁ current is

50 - i₁*(12.5k) - 50k*(i₁-i₂) = 0

( the current through the 12.5k ohm resistor is i₁ and the current through the 50k ohm resistor is the difference of the currents i₁ and i₂ because both the currents flow through it but in opposite directions)

The equation of the mesh currents of the mesh with i₂ current is

50k*(i₂-i₁) - 10k*(i₂) - 75k*i_x = 0

(the current through the 10k ohm resistor is i₂ and the current through the 50k ohm resistor is the difference of the currents i₁ and i₂ because both the currents flow through it but in opposite directions)

In the mesh 1 i₁ current is flowing so i₁ current is dominant than i₂, in a similar way in the mesh 2 i₂ current is flowing so i₂ current is dominant than i₁