Electric Circuits - Mission EC3 Detailed Help

A battery does 6 Joules of work for every 4 C of charge that it encounters during a 2-second time period. What is the voltage of the battery?

Definition of Electric Potential:
Electric potential is a location dependent quantity that expresses the amount of potential energy per unit of charge at a specified location. Mathematically, electric potential is the quantity of energy per unit of charge. Typical units on electric potential are Joules per Coulomb (abbreviated J/C). The term voltage is sometimes used in place of the phrase electric potential. Because of the use of the term voltage, the units of electric potential is the Volt. One volt is equivalent to a J/C.

The role of a battery in an electric circuit is to do work upon an electric charge. By doing work upon the charge, the battery moves charge to a high energy and high potential location. Once there, the charge can naturally move through the external circuit back to the low energy terminal. As mentioned in the Define Help section, electric potential or voltage describes the amount of electric potential energy per unit of charge at a specific location. A 12-volt battery provides 12 Joules of energy for every 1 Coulomb of charge that it moves from the low energy location to the high energy location. This voltage rating simply expresses the ratio of energy per charge. To say such a battery supplies 12 J of energy per 1 C of charge is the same as saying it supplies 24 J of energy per 2 C of charge. As such, the voltage rating of a battery simply describes the energy change per every coulomb of charge that is moved between terminals.

In this question, the time period over which the battery does work on the charge is mentioned. The time period provides additional information about the process. But don't be fooled! The time has little to do with the battery and its voltage. In fact, a 1.5 Volt battery will not always do this 6 J of work on 4 C of charge in 2 seconds. Sometimes the same work will be done on the same charge in a different time period. The time itself is a descriptor of the power of the circuit - the rate at which the devices (bulbs, heaters, motors and other appliances) in the circuit use the electrical energy. The battery provides the energy at the same rate as it is being used up by the devices in the external circuit. If a bulb with a different power rating is placed in this circuit, then the same work will be done on the same amount of charge in a different amount of time.