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# Lecture 3 PowerPoint PPT Presentation

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:

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:

• 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

• 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

• 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

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

• Nodes can be “spread out” by perfect conductors

### Basic Definition – Loop

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

### 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

• 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

• Write KCL at the node below:

### KCL – Example 2

• Use KCL to determine the current i

### 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

• 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

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

### 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

• 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.

### Circuit Analysis – Example 2

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

### 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

• 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