Original question stems from confusion about where exactly the Ohm’s law should be applied and what namely does “\$R\$” refer to.

There are, roughly, three sources of power losses related to transmission, that are determined by:

• current in lines,
• transmission voltage,
• conversion (in a broad sense, AC/AC included).

Losses determined by current are mostly (but not exclusively) due to wire resistance. The Ohm’s law gives \$I^2\cdot R_{\mathrm{wire}}\$, right. But \$I\cdot R_{\mathrm{wire}}\$ has nothing to do with the transmission voltage – is’s the voltage drop in wires.

Losses determined by transmission voltage may play a noticeable rôle in cables, but can be neglected in overhead power lines until the isolation breaks down.

There are also losses directly and indirectly inflicted by conversion. Even a simple transformer has inherent power losses due to its magnetic core. Moreover, a transformer uses an out-of-phase (reactive) AC current that put an additional term to \$I\$ of the line feeding it (hence increasing ohmic losses to some extent). So, unlike the model presented in Transistor’s answer, transformers do not act for free. But, for sufficiently long distances (where \$R_{\mathrm{wire}}\$ is of significant value) and heavy loads stepping the transmission voltage up pays off. Decrease in ohmic losses can be much larger than increase in all other ones.

Original question stems from confusion about where exactly the Ohm’s law should be applied and what namely does “\$R\$” refer to.

There are, roughly, three sources of power losses related to transmission, that are determined by:

• current in lines,
• transmission voltage,
• conversion (in a broad sense, AC/AC included).

Losses determined by current are mostly (but not exclusively) due to wire resistance. The Ohm’s law gives \$I^2\cdot R_{\mathrm{wire}}\$, right. But \$I\cdot R_{\mathrm{wire}}\$ has nothing to do with the transmission voltage – it’s the voltage drop in wires.

Losses due to transmission voltage (such as currents leaking from/between wires) may play a noticeable rôle in cables, but can be neglected in overhead power lines until the isolation breaks down.

There are also losses directly and indirectly inflicted by conversion. Even a simple transformer has inherent power losses due to its magnetic core. Moreover, a transformer uses an out-of-phase (reactive) AC current that put an additional term to \$I\$ of the line feeding it (hence increasing ohmic losses to some extent). So, unlike the model presented in Transistor’s answer, transformers do not act for free. But, for sufficiently long distances (where \$R_{\mathrm{wire}}\$ is of significant value) and heavy loads stepping the transmission voltage up pays off. Decrease in ohmic losses can be much larger than increase in all other ones.

There are, roughly, three sources of power losses related to transmission, that are determined by:

• current in lines,
• voltage in lines,
• conversion (in a broad sense, AC/AC included).

Losses determined by current are mostly (but not exclusively) due to wire resistance. The Ohm’s law gives \$I^2\cdot R_{\mathrm{wire}}\$, right. Losses determined by voltage may play a noticeable rôle in cables, but can be neglected in overhead power lines until the isolation breaks down.

There are also losses directly and indirectly inflicted by conversion. Even a simple transformer has inherent power losses due to its magnetic core. Moreover, a transformer uses an out-of-phase (reactive) AC current that put an additional term to \$I\$ of the line feeding it (hence increasing ohmic losses to some extent). So, unlike the model presented in Transistor’s answer, transformers do not act for free. But, for sufficiently long distances (where \$R_{\mathrm{wire}}\$ is of significant value) and heavy loads stepping the transmission voltage up pays off. Decrease in ohmic losses can be much larger than increase in all other ones.

Original question stems from confusion about where exactly the Ohm’s law should be applied and what namely does “\$R\$” refer to.

There are, roughly, three sources of power losses related to transmission, that are determined by:

• current in lines,
• transmission voltage,
• conversion (in a broad sense, AC/AC included).

Losses determined by current are mostly (but not exclusively) due to wire resistance. The Ohm’s law gives \$I^2\cdot R_{\mathrm{wire}}\$, right. But \$I\cdot R_{\mathrm{wire}}\$ has nothing to do with the transmission voltage – is’s the voltage drop in wires. 

Losses determined by transmission voltage may play a noticeable rôle in cables, but can be neglected in overhead power lines until the isolation breaks down.

There are also losses directly and indirectly inflicted by conversion. Even a simple transformer has inherent power losses due to its magnetic core. Moreover, a transformer uses an out-of-phase (reactive) AC current that put an additional term to \$I\$ of the line feeding it (hence increasing ohmic losses to some extent). So, unlike the model presented in Transistor’s answer, transformers do not act for free. But, for sufficiently long distances (where \$R_{\mathrm{wire}}\$ is of significant value) and heavy loads stepping the transmission voltage up pays off. Decrease in ohmic losses can be much larger than increase in all other ones.