Electrical Energy and Power in Conductors

When current flows through a conductor, charges move in response to a potential difference. As they move, electrical potential energy decreases, and this energy is transferred to the conductor.

In an ideal case without collisions, the lost potential energy would appear as kinetic energy of the charges. In a real conductor, frequent collisions with atoms convert this energy mainly into heat.

Important Point: Electrical energy supplied by the source is not destroyed; it is converted into thermal energy in the resistor.

Consider a conductor with endpoints A and B such that current I flows from A to B and the potential difference is:

If this value is positive, charges move in the direction of decreasing potential energy.

In a small time interval Δt, the amount of charge passing through the conductor is:

This relation connects current with charge flow and forms the base for the derivation of electrical work and power.

The decrease in potential energy of charge ΔQ moving through potential difference V is:

Using ΔQ = I Δt,

Meaning

• The negative sign shows that potential energy decreases.
• The source supplies this energy to the moving charges.
• This is the electrical energy given to the conductor in time Δt.

In an ideal conductor without collisions,

But in real metallic conductors, drift speed remains almost steady because collisions continuously transfer energy to the lattice of atoms. This produces the heating effect of current.

Remember: Current does not heat the wire because charges “store” energy; heating occurs because moving charges lose energy in collisions.

In a real conductor, the energy delivered by the source in time Δt is dissipated as heat:

Here, ΔW is the electrical work done or thermal energy produced in the resistor in time Δt.

Electric power is the rate at which electrical energy is converted into other forms of energy.

So,

This is the basic expression for electric power in any circuit element.

Using Ohm’s law,

Substituting into P = IV:

Also,

Therefore,

Final Formula Set

These are equivalent expressions for power dissipated in an ohmic resistor.

The term ohmic loss refers to the electrical power converted into heat in a resistor, given by P = I²R.

Suppose a device receives power P at voltage V and current I. Then:

If power is transmitted through long cables having resistance R_c, then some power is wasted as heat in the cables:

Using I = P/V,

Conclusion from the formula

• For fixed power P, cable resistance Rc , the power loss decreases when the transmission voltage increases.
• Power loss is inversely proportional to V².
• This is why electricity is transmitted at very high voltage over long distances.