# Why does the electric potential has to drop to 0 at the end of an electric circuit

My question is the following:

In every exemplary circuit, the voltage always equals 0 at the end of electrons "road". I'm aware that the wires are not perfect conductors and they have their built-in resistance as well, but

• what makes the conducting material reduce the voltage to 0?

• What force/phenomenon/mechanism is responsible for the thorough voltage drop?

In other words,

• WHY does the potential drop on each barrier/component has to sum up to the total electric potential between two battery terminals?

I understand that the current is evenly distributed across the whole circuit and it's equal to Voltage divided by the net resistance of the whole circuit, but

• where does it really come from?

It always seemed a bit mysterious to me, like a self-regulating organism.

The question is related to Kirchoff's Law.

The laws are called conservation laws as they are based on conserved quantities. First is that amount of charge in a circuit is conserved. The other one says, that the total energy must be conserved.

Voltage drop to zero is a consequence of the second example, known as voltage law.

To elaborate on your question, let's start from the basic principles.

The force between two charges is given as: $$\vec F=k_e\frac{Qq}{r^2}\hat r$$ From this equation we can find electric field, which roughly measures how strong is E-field at any point. $$\vec E=\frac{\vec F}{q}=k_e\frac{Q}{r^2}\hat r$$ Voltage is defined as potential difference between two points. In simple cases it can be expressed as function that is depended only on an end point and initial point. (if E-field is conservative).

Now all this information will (hopefully!) give you an answer you are looking for.

Since voltage can be expressed as difference in potential between initial point and end point, what would be the voltage if the initial point is the same as final point for simple case? (I.e a closed loop).

$$\Delta V=V(r_f)-V(r_i)\\V(r_f)=V(r_i)$$

The voltage equals 0 because you are comparing it to itself.

Just like the height of a person is always measured from the bottom of her feet to the top of her head, voltage is also measured between two points.

Think of the height of a person. If you sum up the height of the head, neck, upper body, lower body - you'll get the exact same as the whole length of this person, no matter how imperfect he or she is.

It's the same with voltage. When you measure the voltage of a battery, you measure it between the minus terminal and the plus terminal. Looking at the voltage at the "end" is like measuring the voltage with both measuring probes on the minus.

It has to be 0 because you are comparing it to itself.

Voltage is a measure of the potential energy of an electric field, and in the case of a circuit the electric field is generated by the battery. As a charge moves from one point of space to another in the presence of an electric field, its potential energy will change. There is no electric field inside an ideal conductor, so the potential remains constant. The electric field from the battery is not null inside a resistor, so, an electron moving through it experiences a voltage drop. The total voltage drop across several resistors needs to be equal to the voltage difference of the battery ends, a result of the conservative nature of the electric field, that is, regardless of which path you take between the two ends of the battery, either on air or inside a circuit, the total difference on potential obtained by integrating the electric field must be the same.