What is the SI unit of resistance?

State Ohm's law for an ohmic resistor.

On a graph of \(V\) against \(I\), what does the slope represent for an ohmic resistor?

A resistor has \(9.0\,\mathrm{V}\) across it and current \(0.30\,\mathrm{A}\). Find \(R\).

A \(15\,\Omega\) resistor carries \(0.20\,\mathrm{A}\). Find the voltage across it.

A wire has resistivity \(4.0\times10^{-8}\,\Omega\,\mathrm{m}\), length \(3.0\,\mathrm{m}\), and area \(2.0\times10^{-6}\,\mathrm{m^2}\). Find its resistance.

A wire is replaced by another of the same material with three times the length and twice the radius. By what factor does the resistance change?

A device has \(I=0.10\,\mathrm{A}\) at \(2.0\,\mathrm{V}\) and \(I=0.50\,\mathrm{A}\) at \(5.0\,\mathrm{V}\). Explain whether it behaves as a constant-resistance ohmic device over this range.

A cylindrical resistor has fixed volume and material. Derive how its resistance scales with length \(L\), then find the factor change if \(L\) is doubled.

A wire of length \(L\) is made from two materials joined end to end, each occupying length \(L/2\), with resistivities \(\rho_1,\rho_2\) and the same cross-sectional area \(A\). Derive the effective resistance and the equivalent uniform resistivity.