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Understanding Ohm’s Law, Power Conservation, and Kirchhoff’s Laws in Circuit Analysis

This lecture provides a comprehensive review of fundamental electrical principles, including Ohm's Law, power conservation, and Kirchhoff's Laws. Key concepts such as the voltage-current characteristics of resistors and power absorption vs. generation are discussed. Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) are critically examined, along with their applications to circuit analysis. Examples illustrate how to apply these laws to analyze complex circuits, determine currents, voltages, and power in various elements while ensuring energy conservation.

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Understanding Ohm’s Law, Power Conservation, and Kirchhoff’s Laws in Circuit Analysis

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  1. Lecture 3 Review: Ohm’s Law, Power, Power Conservation Kirchoff’s Current Law Kirchoff’s Voltage Law Related educational materials: Chapter 1.4

  2. Review: Ohm’s Law • Ohm’s Law • Voltage-current characteristic of ideal resistor:

  3. Review: Power • Power: • Power is positive if i, v agree with passive sign convention (power absorbed) • Power is negative if i, v contrary to passive sign convention (power generated)

  4. Review: Conservation of energy • Power conservation: • In an electrical circuit, the power generated is the same as the power absorbed. • Power absorbed is positive and power generated is negative

  5. Two new laws today: • Kirchoff’s Current Law • Kirchoff’s Voltage Law • These will be defined in terms of nodes and loops

  6. Basic Definition – Node • A Node is a point of connection between two or more circuit elements • Nodes can be “spread out” by perfect conductors

  7. Basic Definition – Loop • A Loop is any closed path through the circuit which encounters no node more than once

  8. Kirchoff’s Current Law (KCL) • The algebraic sum of all currents entering (or leaving) a node is zero • Equivalently: The sum of the currents entering a node equals the sum of the currents leaving a node • Mathematically: • We can’t accumulate charge at a node

  9. Kirchoff’s Current Law – continued • When applying KCL, the current directions (entering or leaving a node) are based on the assumed directions of the currents • Also need to decide whether currents entering the node are positive or negative; this dictates the sign of the currents leaving the node • As long all assumptions are consistent, the final result will reflect the actual current directions in the circuit

  10. KCL – Example 1 • Write KCL at the node below:

  11. KCL – Example 2 • Use KCL to determine the current i

  12. Kirchoff’s Voltage Law (KVL) • The algebraic sum of all voltage differences around any closed loop is zero • Equivalently: The sum of the voltage rises around a closed loop is equal to the sum of the voltage drops around the loop • Mathematically: • If we traverse a loop, we end up at the same voltage we started with

  13. Kirchoff’s Voltage Law – continued • Voltage polarities are based on assumed polarities • If assumptions are consistent, the final results will reflect the actual polarities • To ensure consistency, I recommend: • Indicate assumed polarities on circuit diagram • Indicate loop and direction we are traversing loop • Follow the loop and sum the voltage differences: • If encounter a “+” first, treat the difference as positive • If encounter a “-” first, treat the difference as negative

  14. KVL – Example • Apply KVL to the three loops in the circuit below. Use the provided assumed voltage polarities

  15. Circuit analysis – applying KVL and KCL • In circuit analysis, we generally need to determine voltages and/or currents in one or more elements • We can determine voltages, currents in all elements by: • Writing a voltage-current relation for each element (Ohm’s law, for resistors) • Applying KVL around all but one loop in the circuit • Applying KCL at all but one node in the circuit

  16. Circuit Analysis – Example 1 • For the circuit below, determine the power absorbed by each resistor and the power generated by the source. Use conservation of energy to check your results.

  17. Example 1 – continued

  18. Circuit Analysis – Example 2 • For the circuit below, write equations to determine the current through the 2 resistor

  19. Example 2 – Alternate approach

  20. Circuit Analysis • The above circuit analysis approach (defining all “N” unknown circuit parameters and writing N equations in N unknowns) is called the exhaustive method • We are often interested in some subset of the possible circuit parameters • We can often write and solve fewer equations in order to determine the desired parameters

  21. Circuit analysis – Example 3 • For the circuit below, determine: (a) The current through the 2 resistor (b) The current through the 1 resistor (c) The power (absorbed or generated) by the source

  22. Circuit Analysis Example 3 – continued

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