# DC Circuits, Mesh Current and Node Voltage Analysis.

Here a few circuits are analysed using mesh current and node voltage analysis.
In the first circuit below containing voltage sources, mesh current analysis is used to derive the 3 loop equations for i1, i2 and i3. Expressed in matrix form, the equations are shown below. In the circuit below containing current sources, node voltage analysis is used to derive the equations for the node voltages V1, V2 and V3. Using the conductance G = 1/R, the node voltage equations expressed in matrix form is shown below. The circuit below has both voltage and current sources. There are different ways in which the equations may be written. Here modified node voltage analysis is used where the current through the voltage source is treated as an unknown. A consequence of this approach is that the number of equations become equal to the number of nodes plus the number of voltage sources. This approach is suitable for numerical analysis but other approaches which use fewer equations and are more suitable for manual analysis are also used. The matrix form of the equations are shown below. Current coming out of the positive terminal of the voltage source is assumed to be positive but some software packages may use a different convention which means the source current comes out with the opposite sign from what obtains here. The applet below shows the solution for the above circuits. Parameter Fn which is set by scrollbar 0 changes the circuit shown. Fn = 0, 1 and 2 shows the solution to the above 3 circuits.

Fn = 3 to 14 shows a random collection of other circuits.