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Lecture 3

Lecture 3. Review: Ohm’s Law, Power, Power Conservation Kirchoff’s Current Law Kirchoff’s Voltage Law Related educational materials: Chapter 1.4. Review: Ohm’s Law. Ohm’s Law Voltage-current characteristic of ideal resistor:. Review: Power. Power:

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Lecture 3

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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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