Consider a wire of lenght $L$ and transversal area $A$ that it isn't an ideal conductor, but follows Ohm's Law. After a few computation we have

$$-\Delta\phi = \rho\frac{L}{A} I $$

where $\rho$ is electrical resistivity. Note that $\Delta\phi < 0$.

My question is if voltage and resistance are defined as:

1. $V =-\Delta\phi$ (positive) and $ R = \rho\frac{L}{A}$ (positive)

or

2. $V = \Delta\phi$ (negative) and $ R =-\rho\frac{L}{A}$ (negative).

Supporting 1): Voltage is the work done by the Electric Field to move a charge from $\mathbf{A}$ to $\mathbf{B}$. And since the difference of potential is the work done by an external force against the Eletric Field from $\mathbf{A}$ to $\mathbf{B}$, I think this definition makes sence.

Supporting 2): I've read in some places (for example, this answer) that voltage is the difference of potential. I could have misunderstood what they meant by that. Also, when I was thought this, I've never been explicitly told what was voltage.

Consider a wire of lenght $L$ and transversal area $A$ that it isn't an ideal conductor, but follows Ohm's Law. After a few computations we have

$$-\Delta\phi = \rho\frac{L}{A} I $$

where $\rho$ is electrical resistivity. Note that $\Delta\phi < 0$.

My question is if voltage and resistance are defined as:

1. $V =-\Delta\phi$ (positive) and $ R = \rho\frac{L}{A}$ (positive)

or

2. $V = \Delta\phi$ (negative) and $ R =-\rho\frac{L}{A}$ (negative).

Supporting 1): Voltage is the work done by the Electric Field to move a charge from $\mathbf{A}$ to $\mathbf{B}$. And since the difference of potential is the work done by an external force against the Eletric Field from $\mathbf{A}$ to $\mathbf{B}$, I think this definition makes sence.

Supporting 2): I've read in some places (for example, this answer) that voltage is the difference of potential. I could have misunderstood what they meant by that. Also, when I was thought this, I've never been explicitly told what was voltage.