# Why does electric potential decrease across a resistor?

If electric potential energy is similar to gravitational potential energy, then shouldn't the potential drop as the charges come nearer to the positive terminal like gravitational potential energy decreases as the object comes nearer to the earth. Also if energy is lost in crossing the resistor, it would imply that the kinetic energy of the charges gets converted into other forms of energy like heat due to the friction between the charges and the resistor, but I don't see how some form of potential energy might be lost in crossing the resistor, and also the current is constant so it also means the kinetic energy of the charges is constant.

• are you asking why the loss of potential is distributed, or what the mechanism for the loss is? – Jasen Dec 25 '19 at 7:08

If there is no resistance charge will accelerate in an electric field. In an ohmic resistor current saturates and is constant as you say correctly. The excess kinetic energy is converted into heat by friction.

The current distributes in such a way that the potential is approximately constant over a cross section of the resistor. Because of current conservation the voltage then drops linearly along the resistor.

Let's assume a conductor of a given length and pass some constant current through it. As we know that there will be loss in energy of the field in the form of heat and we know that : $$E= V/D$$ $$\therefore$$ for a given loss in field and for a fixed distance of the movement of the charge we must get some loss in potential

A rough mechanical analogy that might help is a block sliding down an incline plane with friction at constant velocity. This can occur if the kinetic friction force acting up the plane equals the component of the gravitational force acting down and parallel to the plane. The block loses gravitational potential energy in the form of heat with no change in kinetic energy.

The block moving at constant velocity is analogous to the current, the drop in gravitational potential energy analogous to drop in electrical potential energy, and the friction surface of the incline plane analogous to the resistance.

Hope this helps

When comparing to gravitational potential energy, charges moving along a zero-resistance wire correspond to a ball rolling around on the same shelf. The potential energy is constant at all points.

But charges moving through a component with resistance correspond to a ball falling down from the shelve. The potential energy now changes (it is "spent" or converted into another form of energy).

To your second point, compare the resisting effect of the resistor with air drag of the ball falling through the air. Potential energy is lost (converted into heat), but the kinetic energy doesn't increase. It stays constant.