METHODS OF ANALYSIS Mesh Analysis Nodal analysis

Mesh Analysis An analysis technique to solve electrical circuit where the mesh currents are used as the circuit variables A loop which does not contain any other loops within it meshes R3R3 R1R1 R2R2 V1V1 V2V2

Mesh Analysis An analysis technique to solve electrical circuit where the mesh currents are used as the circuit variables It involves systematic steps with an objective to solve the mesh currents If all mesh currents are known, the circuit can be solved A loop which does not contain any other loops within it i2i2 i1i1 v 1 = R 1 i 1 R3R3 R1R1 R2R2 V1V1 V2V2 + v 1  +v3+v3 v 3 = R 3 (i 1 - i 2 ) v 2 = R 2 i 2 + v 2  ioio i o = (i 1 - i 2 )  mesh current is not branch current ! i 1 & i 2 are mesh currents

Mesh Analysis Mesh analysis only applicable to planar circuit  Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing Planar circuit

Mesh Analysis Mesh analysis only applicable to planar circuit  Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing nonplanar circuit

Mesh Analysis Mesh analysis only applicable to planar circuit  Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing ?

Mesh Analysis Mesh analysis only applicable to planar circuit  Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing ?

Mesh Analysis Step 1 Assign mesh currents to the meshes Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents i1i1 i2i2 22 99 12  44 33 24 V 36 V Step 3 Solve mesh currents in equations obtained in step 2, simultaneously

i1i1 9k  6k  12k  4k  3k  6 V  + i3i3 Mesh Analysis Step 1 Assign mesh currents to the meshes Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents i2i2 Step 3 Solve mesh currents in equations obtained in step 2, simultaneously Example 2

9k  6k  12k  4k  3k  6 V  + Mesh Analysis Example 2 Verification using Pspice Netlist: Mesh example 2 R V1 2 1 DC 6 R R R R DC V PRINT DC I(R1) I(R3), I(R5).END

Mesh Analysis Example 2 Verification using Pspice

++ +  +vo+vo 4k  2k  6k  2k  6 V 3 V i1i1 Mesh Analysis Step 1 Assign mesh currents to the meshes Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents i2i2 Step 3 Solve mesh currents in equations obtained in step 2, simultaneously Example 3 Using mesh analysis, solve v o

i1i1 Mesh Analysis Step 1 Assign mesh currents to the meshes  i 3 is already solved i.e. i 3 = 5A Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents i2i2 Step 3 Solve mesh currents in equations obtained in step 2, simultaneously Example 4 Using mesh analysis, solve v o i3i3 ++ ++ 20 V 40 V 4  8  1  2  5A