Peoples Physics Concepts

http://www.ck12.org Chapter 12. Electricity

12.3 Voltage

• Describe the concept of Voltage and apply it in energy conservation problems.

Students will learn the concept of Voltage and how to apply it in energy conservation problems.

Key Equations

E=−∆∆xV Electric field vs electric potential.

∆UE=q∆V Change in potential energy due to travel through changing voltage.

V=kqr Electric potential of a single charge.

Guidance

Like gravity, the electric force can do work and has a potential energy associated with it. But like we use fields to

keep track of electromagnetic forces, we useelectric potential, orvoltageto keep track of electric potential

energy. So instead of looking for the potential energy of specific objects, we define it in terms of properties of the

space where the objects are.

Theelectric potential difference, orvoltage difference(often just called voltage) between two points (A and B) in

the presence of an electric field is defined as the work it would take to move apositive test charge of magnitude 1

from the first point to the second against the electric force provided by the field. For any other chargeq, then, the

relationship between potential difference and work will be:

∆VAB=

WAB

q

[4] Electric Potential

Rearranging, we obtain:

︸︷︷︸W

Work

= ∆︸ V︷︷AB ︸

Potential Difference

×︸︷︷︸q

Charge

The potential of electric forces to do work corresponds to electric potential energy:

∆UE,AB=q∆VAB [5] Potential energy change due to voltage change

The energy that the object gains or loses when traveling through a potential difference is supplied (or absorbed) by

the electric field — there is nothing else there. Therefore, it follows thatelectric fields contain energy.

To summarize: just as an electric field denotes force per unit charge, so electric potential differences represent

potential energy differencesper unit charge. Voltage is by definition the electric potential energy per Coulomb. So

it is the electrical potential energy value divided by the charge. Thus, voltage difference is the potential value for

potential energy. A 12V battery can not produce energy without charge flowing (i.e. you must connect the two

ends). Electric potential is measured in units of Volts(V)–thus electric potential is often referred to as “voltage.”

Electric potential is the source of the electric potential energy. You can read the electric potential lines (that is the

voltage lines) just like you would a contour map while backpacking in the mountains. Positive charges move

towards lower electric potential; negative charges move toward higher electric potential. Thus, positive charges go

’downhill’ and negative charges go ’uphill’.