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Lesson 10: Nodal Analysis I

Lesson 10: Nodal Analysis I. Learning Objectives. Apply Ohm’s Law using nodal voltages. Apply the Nodal Analysis method to determine an unknown node voltage and branch currents in a simple DC circuit.

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Lesson 10: Nodal Analysis I

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  1. Lesson 10: Nodal Analysis I

  2. Learning Objectives • Apply Ohm’s Law using nodal voltages. • Apply the Nodal Analysis method to determine an unknown node voltage and branch currents in a simple DC circuit

  3. Based on a systematic application of KCL, nodal analysis allows us to obtain a set of simultaneous equations to solve for voltages and current in any linear circuit. Nodal analysis

  4. In nodal analysis we are interested in finding node voltages. Given a circuit with nnodes, Select a reference node. Assign voltages va, vb, vc ….to the remaining nodes. Apply KCL to each node expressing branch currents in terms of node voltages. Solve the resulting simultaneous equations to obtain unknown node voltages. Nodal analysis steps

  5. What are the voltages of the three nodes a,b,c below? 1. Identify the nodes

  6. In nodal analysis, we usually write the branch currents directly in terms of node voltages and branch resistances. Care must be taken in keeping the polarity correct! 2. Write equations for branch currents

  7. 2. Write equations for branch currents • You can make the problem simpler by always arbitrarily assuming current leaves each node • This simplifies writing the resulting equations and prevents polarity errors.

  8. 3. Substitute into KCL and solve for the unknowns

  9. You can solve this with some simple algebra…

  10. Example Problem 1 Solve for node voltage Vb

  11. Example Problem 2 Solve for node voltage Vb

  12. Making it tougher… • The polarity of the voltage supplies changes how you write the equations • Notice the inverted supply on the right and how you write the equation

  13. You can solve this with some simple algebra…

  14. Example Problem 3 How many nodes in the circuit below have unknown voltages? Determine IUNK

  15. Example Problem 4 Find the voltage at node b and the unknown current.

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