Lecture 3
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Lecture 3. Review: Ohm’s Law, Power, Power Conservation Kirchoff’s Current Law Kirchoff’s Voltage Law Related educational modules: Section 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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Lecture 3

Lecture 3

Review:

Ohm’s Law, Power, Power Conservation

Kirchoff’s Current Law

Kirchoff’s Voltage Law

Related educational modules:

Section 1.4


Review ohm s law

Review: Ohm’s Law

  • Ohm’s Law

    • Voltage-current characteristic

      of ideal resistor:


Review power

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)


Review conservation of energy

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


Lecture 3

  • Two new laws today:

    • Kirchoff’s Current Law

    • Kirchoff’s Voltage Law

    • These will be defined in terms of nodes and loops


Basic definition node

Basic Definition – Node

  • A Node is a point of connection between two or more circuit elements

    • Nodes can be “spread out” by perfect conductors


Basic definition loop

Basic Definition – Loop

  • A Loop is any closed path through the circuit which encounters no node more than once


Kirchoff s current law kcl

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


Kirchoff s current law continued

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


Kcl example 1

KCL – Example 1

  • Write KCL at the node below:


Kcl example 2

KCL – Example 2

  • Use KCL to determine the current i


Kirchoff s voltage law kvl

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


Kirchoff s voltage law continued

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


Kvl example

KVL – Example

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


Circuit analysis applying kvl and kcl

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


Circuit analysis example 1

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.


Example 1 continued

Example 1 – continued


Circuit analysis example 2

Circuit Analysis – Example 2

  • For the circuit below, write equations to determine the current through the 2 resistor


Example 2 alternate approach

Example 2 – Alternate approach


Circuit analysis

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


Circuit analysis example 3

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


Circuit analysis example 3 continued

Circuit Analysis Example 3 – continued


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