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Circuit Resistance and Material Resistivity from Ohmic Fields

Recover component resistance from positive circuit measurements, and separately recover material resistivity from electric field and current density, with preserved inverse controls.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 9 V drop with 3 A gives a circuit resistance of 3 Ω and power of 27 W. Local E = 9 V/m with J = 300 A/m² gives material resistivity 0.03 Ω·m.

V = IR; P = VI = I²R; E = ρJ. Circuit resistance R and material resistivity ρ have different dimensions.

Worked example

Enter these known values and leave the other values blank.

Voltage drop magnitude
9 V
Current magnitude
3 A
Local current density magnitude
300 A/m²
Local electric field magnitude
9 V/m
Resistor power
27 W
Circuit resistance
3 Ω
Material resistivity
0.03 Ω·m

Assumptions and limitations

  • Use positive magnitudes for a steady ohmic resistor. This model does not implement zero-current degeneracies, a signed source power convention, reactive AC components or a nonlinear device.
  • The circuit group uses V=IR and P=VI. A positive current inferred from power and resistance uses the principal square root. Any two independent circuit quantities determine the other two; conflicting locked entries produce an error.
  • The local material group uses E=ρJ for an isotropic ohmic material. J is current per cross-sectional area, E is voltage per length and ρ is resistivity in ohm meters. Their selected prefixes retain those dimensions.
  • The two groups are independent here: no conductor length or cross-sectional area connects circuit resistance/current to material resistivity/current density. Supplying circuit values alone does not infer a material resistivity.
  • Resistance is measured in ohms; resistivity is measured in ohm meters. Neither is supplied as a material preset. Use values appropriate to the material, geometry and temperature when applying this idealized model.
  • Power in watts is energy per time, not total energy in joules. This calculation does not size wiring, model thermal limits or establish a device power rating.

Common questions

Can voltage and power determine resistance?

For the positive resistor model, resistance equals voltage squared divided by power. Enter those two independent quantities and leave resistance blank.

Why is material resistivity not the same value as circuit resistance?

They have different units and depend on different inputs. Relating them requires conductor length and cross-sectional area, which are not guessed here.

Does a resistor network have an equivalent resistance?

A linear series or parallel network can be represented by an equivalent component resistance. This tool uses that supplied equivalent value; it does not infer a network topology.

References

Label every local current density in amperes per square meter, local electric field in volts per meter and material resistivity in ohm meters for every retained prefix and remove the now-redundant separate dimensional suffix, keeping circuit current/voltage/resistance units separate. Require strictly positive magnitudes with sign-based validation; retain all twelve inverse branches and the two independent circuit/material groups.

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