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Electric Potential Difference (Voltage). Ohm's Law

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15.3Electric Potential Difference (Voltage). Ohm's Law


In these revision notes for Electric Potential Difference (Voltage). Ohm's Law, we cover the following key points:

  • What is the scientific definition of electric potential?
  • Why potential difference is more important that the electric potential itself?
  • Why the potential difference produced by a battery is different from the potential difference produced by a charged object?
  • What is the electromotive force?
  • What are the common things and the differences between electromotive force and potential difference as concepts?
  • What does Ohm's Law for a part of a circuit say?
  • What is the general form of Ohm's Law for the whole circuit?

Electric Potential Difference (Voltage). Ohm's Law Revision Notes

Electric potential is defined as the electric potential energy per unit charge. The equation of electric potential is

V = k ∙ Q/r

where Q is the charge that produces the electric field and r is the distance from that charge, at which we want to calculate the electric potential V.

The unit of electric potential, i.e. Volt [V]. Given that the electric potential of a trial charge Q0 located inside the electric field produced by the charge Q at the distance r from it, is

V=W/Q0

where W is the electric potential energy of the trial charge at the given distance, we obtain for the unit of electric potential

[V]=[J/C]

A more practical definition for the electric potential is

"Electric potential V, is the work done by an electric force to bring a positive test charge Q0 from infinity at a given distance r from another positive charge Q."

The potential difference in a circuit is also known as voltage.

Electric charges flow from places of higher potential in places of lower potential. This flow stops when the potential is balanced.

We say a battery is a source of electricity but not because it generates free electrons; rather, a battery simply pushes the electrons of the conducting wire by making them flow throughout the circuit. As a result, a potential difference between the terminals of the battery is produced, which is the main factor that causes the flow of charges throughout the circuit. Without this potential difference, no charge would flow through the circuit, regardless the number of free charges available.

A battery is composed by two or more cells. A cell is a single unit device, which converts chemical energy into electric energy. A battery usually consists of a group of cells.

By definition, electromotive force (emf) is the energy supplied to the unit charge by a cell or battery (electric source).

Mathematically, we have

emf=Wsource/Q

Electromotive force exists only at the source; it represents the maximum potential difference a battery can generate while potential difference can be calculated between any two points of the circuit (usually between the extremities of an electric consumer installed in the circuit. Numerically, electromotive force is greater than the actual potential difference as electromotive force represents the maximum potential difference possible.

Ohm's Law is states that:

The current passing through a circuit component is directly proportional to the potential difference applied across it.

The mathematical expression of Ohm's Law for a part of circuit is:

I=∆V/R

Ohm's Law for the whole circuits is written as

emf=I ∙ (r + R + Rw)

where r is the resistance of battery, R is the resistance of the circuit component and Rw is the resistance of the conducting wire.

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