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Ohmic Current, Power and Local Material Fields

Relate positive voltage, current, resistance and power alongside a separate electric-field, current-density and material-resistivity model, with editable 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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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 12 V drop across 6 Ω gives 2 A and 24 W. Separately, E = 6 V/m and J = 200 A/m² imply ρ = 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
12 V
Circuit resistance
6 Ω
Local current density magnitude
200 A/m²
Local electric field magnitude
6 V/m
Resistor power
24 W
Current magnitude
2 A
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

Why does changing current not determine current density?

Current density needs a cross-sectional area. This tool preserves a separate local material relationship, so it does not guess that missing geometry.

Can I recover current from power?

Enter positive power and either voltage or resistance. Current is P/V or the positive square root of P/R under the stated resistor model.

Are resistance and resistivity interchangeable?

No. Resistance describes a component and has units Ω. Resistivity describes a material response and has units Ω·m; geometry is needed to relate them.

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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