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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

- Ohm’s Law
- Voltage-current characteristic
of ideal resistor:

- Voltage-current characteristic

- 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)

- 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

- A Node is a point of connection between two or more circuit elements
- Nodes can be “spread out” by perfect conductors

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

- 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

- 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

- Write KCL at the node below:

- Use KCL to determine the current i

- 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

- 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

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

- 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

- 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.

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

- 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

- 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