Ohm's Law (2.1) Kirchhoff's Laws (2.2)

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Ohm's Law (2.1)Kirchhoff's Laws (2.2)

• Prof. Phillips
• January 24, 2003

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Resistors

• A resistor is a circuit element that dissipates
  electrical energy (usually as heat)
• Real-world devices that are modeled by resistors
  incandescent light bulbs, heating elements
  (stoves, heaters, etc.), long wires
• Resistance is measured in Ohms (W)

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Ohms Law

• v(t) i(t) R - or - V I R
• p(t) i(t)v(t) i2(t) R v2(t)/R
• Always dissipating or absorbing power (pgt0)

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Example a 25W Bulb

• If the voltage across a 25W bulb is 120V, what is
  its resistance?
• R V2/P (120V)2/25W 576 ?
• What is the current flowing through the 25W bulb?
• I V/R 120V/576 ? 0.208 A 208 mA

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Thought Question

• When I measured the resistance of a 25W bulb, I
  got a value of about 40W. Whats wrong here?
• Answer The resistance of a wire increases as
  the temperature increases. For tungsten, the
  temperature coefficient of resistivity is
  4.5x10-3/oK. A light bulb operates at about
  5000oF.

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Open Circuit

• What if R??
• i(t) v(t)/R 0

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Short Circuit

• What if R0?
• v(t) i(t) R 0

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Class Example
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Kirchhoffs Laws

• Kirchhoffs Current Law (KCL)
• sum of all currents entering a node is zero
• sum of currents entering node is equal to sum of
  currents leaving node
• Kirchhoffs Voltage Law (KVL)
• sum of voltage (drops) around any loop in a
  circuit is zero

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KCL (Kirchhoffs Current Law)
i1(t)
i5(t)
i2(t)
i4(t)
i3(t)

• The sum of currents entering the node is zero
• Analogy mass flow at pipe junction

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Class Examples
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KVL (Kirchhoffs Voltage Law)



v2(t)

v1(t)
v3(t)

• The sum of voltages around a loop is zero
• Analogy pressure drop thru pipe loop

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KVL Polarity

• A loop is any closed path through a circuit in
  which no node is encountered more than once
• Voltage Polarity Convention
• A voltage encountered to - is positive
• A voltage encountered - to is negative

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Class Examples
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Electrical Analogies (Physical)
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EE Subdisciplines

• Communication/Signal Processing
• Controls
• Electronic Circuits
• Electromagnetics
• Power
• Solid State

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Power

• Generation of electrical energy
• Storage of electrical energy
• Distribution of electrical energy
• Rotating machinery-generators, motors

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Electromagnetics

• Propagation of electromagnetic energy
• Antennas
• Very high frequency signals
• Fiber optics

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Communications/Signal Proc.

• Transmission of information electrically and
  optically
• Modification of signals
• enhancement
• compression
• noise reduction
• filtering

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Controls

• Changing system inputs to obtain desired outputs
• Feedback
• Stability

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Solid State

• Devices
• Transistors
• Diodes (LEDs, Laser diodes)
• Photodetectors
• Miniaturization of electrical devices
• Integration of many devices on a single chip

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Digital

• Digital (ones and zeros) signals and hardware
• Computer architectures
• Embedded computer systems
• Microprocessors
• Microcontrollers
• DSP chips

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Personal Systems Scaling