Mesh Current Method

Mesh Current Method - Mesh Current Technique Of...

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Unformatted text preview: Mesh Current Technique Of Circuit Analysis DePiero EE 201 Learning Objec@ves •  Analyze circuits containing both independent and dependent sources using mesh current analysis. •  Notes: –  Mesh analysis most convenient for circuits containing voltage sources. –  Voltage sources will be addressed before current sources –  Dependent sources will not be addresses ini=ally Mesh Current Method is Systema@c •  Yields a set of simultaneous equa@ons from which unknown current and voltages may be found. •  Should work for any circuit… –  Pathological cases may exist. (No worries). •  Simultaneous equa@ons may be solved via Cramer’s Rule, or directly on a calculator. –  See Appendix A for Cramer’s Rule. Mesh Current Analysis  ­ Ini=al Version •  1) Define the currents around each mesh in the same direc@on (clockwise). •  2) Apply KVL around each mesh. Express each KVL voltage, Vn, in terms of one or more mesh currents. Use the passive sign conven@on. •  3) Solve KVL equa@ons simultaneously. Example 1 •  Find power (delivered or absorbed) by the 8 V source. •  1) Define mesh currents •  2) KVL for meshes –  Assign V polarity to resistors –  Sum Vn = 0 •  3) Solve for mesh currents •  Find power for 8 V source Left mesh current (CW) = 4A Right mesh current (CW) = -1/3A Branches Sharing Mesh Currents Require Special A]en@on •  Consider the net current (downward) for the 8V source •  Net current is I1 – I2 I1 I2 Branches Sharing Mesh Currents Require Special A]en@on… •  Suppose the upper terminal of the 1 ­Ohm resistor is (+). •  What mesh currents would result in given polarity for the 1 ­Ohm resistor? •  Mesh currents: I1 – I2 I1 I2 Mesh Current Analysis – Full Version •  1) Define the currents around each mesh in the same direc@on (clockwise). •  2) If a current source is present –  Define Vx as the voltage across it. The polarity for Vx is arbitrary, but should remain unchanged in all KVL equa@ons. –  Use KCL to create another equa@on, rela@ng mesh currents to current of the current source. •  3) Apply KVL around each mesh. Express each KVL voltage, Vn, in terms of one or more mesh currents. Use the passive sign conven@on. •  4) If dependent sources are present, add another equa@on based on the defini@on of the dependent source. •  5) Solve KVL equa@ons simultaneously. ...
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