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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