Resistor Calculator

Resistance, resistivity, equivalent resistance and power rating with step-by-step solutions

Find the equivalent resistance of 100 ohm in series with 220 ohm parallel to 330 ohm

Find the resistance of 25 m of copper wire with a 1.6 mm diameter

Find the power dissipated by a 470 ohm resistor carrying 45 mA

What resistance gives 20 mA from a 5 V supply?

Resistance from Resistivity: R = ρL/A

A conductor's resistance follows from the material and the geometry:

$R = \\frac{\\rho L}{A} \\qquad A = \\frac{\\pi d^2}{4}$

Symbols and SI units:

$R$ — resistance, ohms (Ω)
$\\rho$ — resistivity, a material property, ohm-metres (Ω·m)
$L$ — conductor length, metres (m)
$A$ — cross-sectional area, square metres (m²)
$d$ — conductor diameter, metres (m)

At 20 °C, copper is $1.68 \\times 10^{-8}$ Ω·m and aluminium $2.65 \\times 10^{-8}$ Ω·m.

The operating assumption: a uniform cross-section at a stated temperature, carrying DC or low-frequency AC. At high frequency the skin effect pushes current to the surface and the effective resistance rises.

The mistake people make: quoting a cable size in mm² and then a length in metres but a diameter in millimetres. Convert everything to metres first, or work consistently in Ω·mm²/m.

Series, Parallel and Power Rating

Resistors in series carry one current and their resistances add; resistors in parallel share one voltage and their conductances add:

$R_s = R_1 + R_2 + \\cdots \\qquad \\frac{1}{R_p} = \\frac{1}{R_1} + \\frac{1}{R_2} + \\cdots$

For exactly two in parallel the product-over-sum shortcut applies:

$R_p = \\frac{R_1 R_2}{R_1 + R_2}$

A parallel combination is always smaller than the smallest branch — a useful sanity check.

The power a resistor must get rid of is

$P = I^2 R = \\frac{V^2}{R} \\quad [\\text{W}]$

Common practice is to run a resistor at no more than about half its rated power so it stays cool. Treat that as orientation only: the binding limit is the manufacturer's derating curve for the actual ambient temperature and mounting.

The mistake people make: inverting only once. $1/R_p$ is the sum of reciprocals — you still have to invert the total at the end.

Common Mistakes to Avoid

Forgetting the final reciprocal — $1/R_p = 0.0136$ means $R_p = 73.5$ Ω, not $0.0136$ Ω.
Mixing prefixes — $4.7$ kΩ is $4700$ Ω and $1.2$ MΩ is $1.2 \\times 10^{6}$ Ω.
Confusing resistance with resistivity — resistivity is a property of the material in Ω·m; resistance is a property of the particular piece of wire.
Using the radius in $A = \\pi d^2/4$ — that formula wants the diameter; with the radius use $A = \\pi r^2$ .
Ignoring temperature — copper rises about $0.393\\%$ per °C, so a conductor at $75$ °C has roughly $22\\%$ more resistance than at $20$ °C.
Sizing a package from average power — a pulsed load can exceed the rating instantaneously even when the average looks safe.
Reading the tolerance band as a digit — the gold or silver band is tolerance, not a value.

示例题目

Step 1: Convert the diameter:

d = 1.6\\ \\text{mm} = 1.6 \\times 10^{-3}\\ \\text{m}

Step 2:

A = \\pi d^2/4 = \\pi (1.6 \\times 10^{-3}\\ \\text{m})^2/4 = \\pi (2.56 \\times 10^{-6}\\ \\text{m}^2)/4 = 2.011 \\times 10^{-6}\\ \\text{m}^2

Step 3:

R = \\rho L/A = (1.68 \\times 10^{-8}\\ \\Omega\\cdot\\text{m})(25\\ \\text{m}) \\div (2.011 \\times 10^{-6}\\ \\text{m}^2)

Step 4: Numerator:

4.20 \\times 10^{-7}\\ \\Omega\\cdot\\text{m}^2

Step 5:

R = (4.20 \\times 10^{-7}) \\div (2.011 \\times 10^{-6}) = 0.209\\ \\Omega

Answer:

R \\approx 0.209

Step 1: Parallel pair:

R_p = (220\\ \\Omega)(330\\ \\Omega) \\div (220\\ \\Omega + 330\\ \\Omega) = 72600 \\div 550 = 132\\ \\Omega

Step 2: Check:

132\\ \\Omega

is smaller than

220\\ \\Omega

, as a parallel combination must be

Step 3: Series total:

R_{eq} = 100\\ \\Omega + 132\\ \\Omega = 232\\ \\Omega

Step 4:

I = V/R_{eq} = 12\\ \\text{V} \\div 232\\ \\Omega = 0.05172\\ \\text{A} = 51.7\\ \\text{mA}

Step 5:

V_p = IR_p = (0.05172\\ \\text{A})(132\\ \\Omega) = 6.83\\ \\text{V}

Step 6: Check:

V_{100} = (0.05172)(100) = 5.17\\ \\text{V}

, and

5.17 + 6.83 = 12.0\\ \\text{V}

Answer:

R_{eq} = 232

Ω,

I \\approx 51.7

mA,

V_p \\approx 6.83

Step 1: Convert the current:

45\\ \\text{mA} = 0.045\\ \\text{A}

Step 2:

V = IR = (0.045\\ \\text{A})(470\\ \\Omega) = 21.2\\ \\text{V}

Step 3:

P = I^2R = (0.045\\ \\text{A})^2 (470\\ \\Omega) = (2.025 \\times 10^{-3}\\ \\text{A}^2)(470\\ \\Omega)

Step 4:

P = 0.952\\ \\text{W}

Step 5: At the usual half-rating practice this needs a

2

W package; confirm against the manufacturer's derating curve for the actual ambient temperature

Answer:

V \\approx 21.2

P \\approx 0.95

W — a

2

W package

常见问题

From a measurement, use Ohm's law R = V/I with volts and amperes. From the conductor itself, use R = rho L / A, with the resistivity in ohm-metres, the length in metres and the cross-sectional area in square metres.

Rearranging R = rho L / A gives rho = RA/L, in ohm-metres. Resistivity is a property of the material at a stated temperature, while resistance also depends on how long and how thick the particular conductor is.

In series the resistances add: R = R1 + R2 + ... In parallel the reciprocals add: 1/R = 1/R1 + 1/R2 + ..., and you must invert the sum at the end. For two resistors in parallel, R = R1R2/(R1+R2).

Work out P = I squared R or V squared / R in watts, then pick a package comfortably above it, since a resistor run near its rating gets hot. The actual allowable dissipation comes from the manufacturer's derating curve for the ambient temperature and mounting, not from the headline number alone.

Resistor Calculator

Resistance, resistivity, equivalent resistance and power rating with step-by-step solutions

Resistance from Resistivity: R = ρL/A

Series, Parallel and Power Rating

Common Mistakes to Avoid

示例题目

常见问题

How do I calculate resistance?

What is the resistivity formula?

How do I find equivalent resistance in series and parallel?

What power rating does my resistor need?

相关求解器

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Resistor Calculator

Resistance, resistivity, equivalent resistance and power rating with step-by-step solutions

Resistance from Resistivity: R = ρL/A

Series, Parallel and Power Rating

Common Mistakes to Avoid

示例题目

Problem: FindtheresistanceofFind the resistance of Findtheresistanceof25mofcopperwireofdiameterm of copper wire of diametermofcopperwireofdiameter1.6mm,takingmm, takingmm,taking\rho = 1.68 \times 10^{-8}Ω⋅m. Ω·m.Ω⋅m.

常见问题

How do I calculate resistance?

How do I calculate resistance?

What is the resistivity formula?

What is the resistivity formula?

How do I find equivalent resistance in series and parallel?

How do I find equivalent resistance in series and parallel?

What power rating does my resistor need?

What power rating does my resistor need?

相关求解器

免费试用 AI-Math