1. What is a Supermesh? one larger mesh created from two or more meshes that have an independent or dependent current source in common reduces the number of KVL loops and allows KVL to be applied around the periphery of the supermesh

2. Mesh 2 Mesh 3 Mesh 1 1. Identify Meshes 1k  2k  12V4mA 2mA I0I0 +–+–

3. I1I1 I2I2 I3I3 1k  2k  12V4mA 2mA I0I0 +–+– 2. Assign Mesh Currents

4. 3.Write mesh equations 1k  2k  12V4mA 2mA I0I0 I1I1 I2I2 I3I3 The Super mesh surrounds this source! The Supermesh does not include this source! +–+– KVL Around the Super mesh +12V – (I3) 2kΩ - (I3 - I2)1k Ω - (I1 - I2)2k Ω = 0 Or (I3) 2k Ω + (I3 - I2)1k Ω + (I1 - I2)2k Ω = 12V and I2 = -4mA Also I1 – I3 = 2mA

5. Solution I 1 = 1.2 mA I 2 = – 4 mA I 3 = – 0.8 mA I 0 = I 1 – I 2 = 5.2 mA

6. Supermesh Example No KVL possible for meshes 1 or 2 Use Supermesh (dotted loop) for KVL

7. Supermesh: Example Supermesh KVL: Mesh 3 KVL: +Vs1 – I1 Ra – I2 Rb + Vs2 –(I2-I3)Rd – (I1-I3)Rc=0

8. Supermesh with Numerical Values