Which of the following is the resistance of the wire ?
\(R=\dfrac{V}{I}\)
Resistance is the ratio of potential difference to current, option 3 :
\(R=\dfrac{V}{I}\)
Ohm’s law. Stated by Georg Simon Ohm in 1827, it says that the current through a conductor is directly proportional to the potential difference across it, provided the physical conditions — temperature above all — remain unchanged :
\(V\propto I\qquad\Rightarrow\qquad V=IR\qquad\Rightarrow\qquad R=\dfrac{V}{I}\)
The constant of proportionality R is the resistance, measured in ohms. One ohm is the resistance of a conductor through which one ampere flows when one volt is applied across it.
Checking the options by dimensions. Resistance has the unit volt per ampere. Option 1, the product IV, is power in watts. Options 2 and 4 are ampere per volt, which is conductance, measured in siemens — the reciprocal of resistance. Option 2 also carries a stray factor of 2 that corresponds to nothing physical. So only option 3 is even of the right kind.
| Expression | What it actually is |
|---|---|
| IV | Electrical power, in watts |
| I/V | Conductance, in siemens |
| I/2V | Half the conductance — no physical meaning |
| V/I | Resistance, in ohms |
What resistance depends on. For a wire of length l and cross-sectional area A :
\(R=\rho\dfrac{l}{A}\)
where ρ is the resistivity of the material. So resistance rises with length and falls as the wire is made thicker, and it depends on the material and on temperature — rising with temperature for metals, and falling for semiconductors.
Hence, the answer is R = V/I.
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