Ohm's Law (2.1) Kirchhoff's Laws (2.2)
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Transcript of 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 ()
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Ohm’s 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 (p>0)
The Rest of
the Circuit
R v(t)
i(t)+
–
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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 40. What’s 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
The Rest of
the Circuit
v(t)
i(t)=0+
–
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Short Circuit
• What if R=0?
• v(t) = i(t) R = 0
The Rest of
the Circuit
v(t)=0
i(t)+
–
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Class Example
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Kirchhoff’s Laws
• Kirchhoff’s 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
• Kirchhoff’s Voltage Law (KVL)
– sum of voltage (drops) around any loop in a circuit is zero
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KCL (Kirchhoff’s Current Law)
The sum of currents entering the node is zero:
Analogy: mass flow at pipe junction
i1(t)
i2(t) i4(t)
i5(t)
i3(t)
n
jj ti
1
0)(
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Class Examples
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KVL (Kirchhoff’s Voltage Law)
• The sum of voltages around a loop is zero:
• Analogy: pressure drop thru pipe loop
0)(1
n
jj tv
v1(t)
+ +–
–
v2(t)v3(t)
+–
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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)
Electrical Hydraulic
Junction/Node Law
KCL: Σ I = 0 Σ G = 0
Loop Law KVL: Σ V = 0 Σ Δp = 0
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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