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MECA Electronics

Resistors, Resistance, Resistivity (ρ) Calculations

Examples of Resistor Packages, Lead, and Mounting Styles - RF CafeReal-world inductor model with resistance, inductance, and capacitance - RF CafeResistors are passive devices used in electronic circuits to control the flow of current. An ideal resistor has no associated stray capacitance or inductance, and therefore performs exactly the same in a direct current (DC) circuit as it does in an alternating current (AC) circuit at any frequency.

Metal | Substance
(Wikipedia table)
Resistivity (ρ) at 20°C
Ohm•Meters (Ω•m)
Aluminum 2.65 x 10-8
Antimony 3.92 x 10-7
Bismuth 1.29 x 10-6
Brass 0.6 - 0.9 x 10-7
Cadmium 6.84 x 10-8
Calcium 3.36 x 10-8
Carbon (amorphous) 5.0-8.0 x 10-4
Carbon (diamond) 1.00 x 1012
Carbon (graphite) 2.5-5.0 x 10-6 (para.)
3.0 x 10-3 (perp.)
Cobalt 6.25 x 10-8
Constantan 4.90 x 10-7
Copper 1.68 x 10-8
Copper (annealed) 1.72 x 10-8
Gold 2.44 x 10-8
Carbon 1 x 10-5
Gallium 1.40 x 10-7
Germanium 4.60 x 10-1
Glass 1.0 x 1011 to 15
Iron 9.71 x 10-8
Lead 2.20 x 10-7
Lithium 9.28 x 10-7
Manganin 4.82 x 10-7
Nichrome 1.10 x 10-6
Mercury 9.80 x 10-7
Nickel 6.99 x 10-8
Palladium 1.08 x 10-7
Platinum 1.06 x 10-7
Quartz (fuzed) 7.50 x 1017
Rubber (hard) 1.0 x 1013
Silicon 6.40 x 102
Silver 1.59 x 10-8
Steel (carbon) 1.43 x 10-7
Steel (stainless) 6.90 x 10-7
Tantalum 1.24 x 10-7
Teflon 1.0 x 1023 to 25
Tin 1.09 x 10-7
Titanium 4.20 x 10-7
Tungsten 5.60 x 10-8
Water (Drinking) 2.0 x 101 to 3
Water (Sea) 2.00 x 10-1
Zinc 5.90 x 10-8

Real-world resistors made of physical components exhibit more than just a pure resistance when present in an AC circuit. A common circuit simulator model is shown to the left. It includes the actual ideal resistor with a parallel capacitive component representing inter-element (if present) mutual capacitance, and a series inductive component representing lead and/or solder/bond pads that respond to

alternating current. SPICE-type simulators use this or an even more sophisticated model to facilitate more accurate calculations over a wide range of frequencies.

Equations (formulas) for combining inductors in series and parallel are given below.

Resistivity of Common Metals

Parallel-Connected Resistors
Inductors in Parallel Formula - RF Cafe
Parallel-connected resistor drawing - RF Cafe

Total resistance of parallel-connected resistors is equal to the reciprocal of the sum of the reciprocals of the individual resistances. Keep units constant.

Series-Connected Resistors

Inductors in Series Formula - RF Cafe
Series-connected resistor drawing - RF Cafe

Total resistance of series-connected resistors is equal to the sum of the individual resistances. Keep units constant.

Windfreak Technologies
Antenna Test Lab - RF Cafe
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    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

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