ECE 221 Electric Circuit Analysis I Chapter 3 SI Notation, Units, Unit Conversion Herbert G. Mayer, PSU & CCUT Status 10/2/2015 Taken with permission from Prof. Phillip Wong @ PSU ECE

Syllabus Scientific Engineering Notation Dimensions Physical Quantities Units

Scientific & Engineering Notation Scientific notation is a compact method for expressing very small or very large numbers. Format: The mantissa conveys the number’s value and accuracy The base and exponent define the scaling factor exponent mantissa base Scientific Engineering exponent multiple of 1 multiple of 3 mantissa -10 < a < 10 -1000 < a < 1000 2

Example: Number Scientific Engineering 0.000001234567 1.23456710-6 0.00001234567 1.23456710-5 123.456710-3 0.0001234567 1.23456710-4 12.3456710-3 0.001234567 1.23456710-3 0.01234567 1.23456710-2 0.1234567 1.23456710-1 1.234567 12.34567 1.23456710 123.4567 1.234567102 1234.567 1.234567103 12345.67 1.234567104 12.34567103 123456.7 1.234567105 123.4567103 1234567 1.234567106 3

Describing Physical Quantities A physical quantity has three components: Dimension (e.g., length, time, etc.) Magnitude (quantity) Unit (reference amount) Example: 12.5 m A measurement determines the number of multiples of a unit that are contained within a physical quantity unit  length magnitude

Dimensions Dimensions describe physical quantities Dimensions are independent of units Each dimension may have a variety of units Dimensions are divided into two areas: Fundamental (e.g., Length L or Time t) Derived (e.g., Velocity = Length / Time)

Units Commonly used unit systems: Metric (decimal: meter, kilogram, second) Engineering System (US: foot, pound-force, second) Système International d′Unités (SI) is the adopted world standard, except United States

SI Supplementary Units SI Base Units Length: meter (m) Time: second (s) Mass: kilogram (kg) Electric current: ampere (A) Temperature: kelvin (K) Amount of substance: mole (mol) Luminous intensity: candela (cd) SI Supplementary Units Plane angle: radian (rad) Solid angle: steradian (sr)

SI Unit Prefixes 1024 yotta Y 10-1 deci d 1021 zetta Z 10-2 centi c 1018 exa E 10-3 milli m 1015 peta P 10-6 micro  1012 tera T 10-9 nano n 109 giga G 10-12 pico p 106 mega M 10-15 femto f 103 kilo k 10-18 atto a 102 hecto h 10-21 zepto z 101 deka da 10-24 yocto y

Commonly used electrical engineering units Resistance (ohm): MΩ kΩ Ω mΩ μΩ nΩ Inductance (henry): kH H mH μH nH pH Capacitance (farad): kF F mF μF nF pF fF aF Voltage (volt): MV kV V mV μV nV Current (ampere): MA kA A mA μA nA pA fA Power (watt): MW kW W mW μW nW pW Frequency (hertz): THz GHz MHz kHz Hz mHz Wavelength (m): km m cm mm μm nm 9

Multipliers for SI Prefix Conversion M→106, k→103, 1, m→10-3, →10-6, n→10-9, p→10-12, f→10-15 Example: 0.01 F = ? pF 0.009 mV versus 40.5 V. Which one is bigger? → (0.009 mV)(103 V/mV) = 9 V.  40.5 V is bigger. From ↓ To → Multipliers for SI Prefix Conversion M k 1 m  n p f 103 106 109 1012 1015 1018 1021 10-3 10-6 10-9 10-12 10-15 10-18 10-21 → (0.01 F)(106 pF/F) = 10000 pF 10

Example: Frequency & Wavelength for EM Waves Electromagnetic waves: (n=10-9, M=106, G=109, T=1012, P=1015, E=1018) Speed of light Name Frequency f Wavelength  Radio 3 Hz – 300 GHz 100 Mm – 1 mm Microwave 300 MHz – 300 GHz 1 m – 1 mm Infrared 300 GHz – 405 THz 1 mm – 750 nm Visible 405 THz – 790 THz 750 nm – 390 nm Ultraviolet 790 THz – 30 PHz 400 nm – 10 nm X-Ray 30 PHz – 30 EHz 10 nm – 0.01 nm Gamma ray more than 30 EHz Less than 0.01 nm 11

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