lecture 3 review: ohm’s law, power, power conservation kirchoff’s current law kirchoff’s...
TRANSCRIPT
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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
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Review: Ohm’s Law
• Ohm’s Law• Voltage-current characteristic of ideal resistor:
)t(iR)t(v
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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)
)t(i)t(v)t(p
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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
0elements All
p
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• Two new laws today:
• Kirchoff’s Current Law
• Kirchoff’s Voltage Law
• These will be defined in terms of nodes and loops
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Basic Definition – Node• A Node is a point of connection between two or more
circuit elements• Nodes can be “spread out” by perfect conductors
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Basic Definition – Loop• A Loop is any closed path through the circuit which
encounters no node more than once
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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
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1
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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
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KCL – Example 1
• Write KCL at the node below:
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KCL – Example 2
• Use KCL to determine the current i
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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
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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
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KVL – Example• Apply KVL to the three loops in the circuit below. Use the
provided assumed voltage polarities
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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
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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.
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Example 1 – continued
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Circuit Analysis – Example 2• For the circuit below, write equations to determine the
current through the 2 resistor
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Example 2 – Alternate approach
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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
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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
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Circuit Analysis Example 3 – continued