Ohm's Law and transmission of electricity

Electricity is transmitted at high voltages. It is said that this reduces current and consequently resistance. But according to ohms law, low current must face high resistance. How is this contradiction possible?

Resistivity is a property of materials, and thus, resistance is a property of the material too, at least for most practical purposes. So $$R$$ is a fixed value for a certain device. In particular, for the wires that transport electricity.

Since Ohm's law holds:

$$V=I\cdot R$$

If you apply more voltage, you will have more current. As in any other wire.

This must not be confused with the transformers. Transformers apply conservation of power (with relatively high efficiency), and power is $$P=V\cdot I$$.

$$V_1\cdot I_1 = V_2 \cdot I_2$$

Energy is generated in power plants. The power plants supply a fixed value $$P_1=V_1\cdot I_1$$. You can only control the exit. $$V_2\cdot I_2=constant$$. If you want more voltage, you'll have decreased current, and vice-versa.

Those ifnal values $$V_2, I_2$$ are then transmitted to wires.

• how can low current face low resistance, which is not possible by ohms law Dec 31 '18 at 18:15
• @MohammadNoorAlam, not every load on the power grid is a resistor. Dec 31 '18 at 18:47
• Indeed. The wires are usually driver from transformer to transformer. If you only look at the wire, you're not seeing the entire circuit. Dec 31 '18 at 19:06

It is said that this reduces current and consequently resistance.

This is wrong. The resistance of the cable does not depend on the current through it (at least not so much that it would matter here).

The reduced current leads to reduced dissipated power in the wire.

Not every load on the power grid is a resistor. So not every load obeys Ohm's Law.

In particular, the load on a high-voltage circuit in the power grid is likely to be a transformer. Here, the left side of the transformer is called the primary side, and the right side is called the secondary side. Two main parameters of the transformer design are the number of turns of wire around the primary side of the core, $$N_P$$, and around the secondary side, $$N_S$$.

The (ideal) transformer is governed by the rules

$$V_S = \frac{N_S}{N_P}V_P$$

and

$$I_P = \frac{N_S}{N_P}I_S.$$

Notice that this means that $$V_P I_P = V_S I_S$$, so that the power delivered to the load on the secondary is equal to the power delivered by the generator to the primary of the transformer.

Using a transformer, a low-resistance load (like dozens or hundreds of light bulbs connected in parallel) can be transformed to appear to the generator as a much higher resistance. Thus power is delivered with much lower currents in the primary circuit than in the secondary circuit, and resistive losses in the primary circuit are reduced.