Electric potential energy is the work needed to move an electric charge from one point in a field to another. The amount of electric potential energy depends on how far apart the two points are and the type of field that exists between them. Electric potential energy can be calculated with this formula:
E=qV, where q is equal to charge in coulombs and V is voltage in volts.
This equation states that the electric potential energy is equal to the charge of a coulomb times volts. The strength of an electric field, V, can be calculated with this formula:
V=E/q, where E is voltage in volts and q is the amount of charge in coulombs
The unit for measuring voltage is called a volt (V), which equals one joule per Coulomb(C). One Joule per Coulomb = J/C. In addition to being related to work done by moving electrons from I to f, electric potential energy can also be used when considering how much heat will be generated if there are two different resistors connected together under an applied current. For example: If a resistor has half the resistance of another, then it will take twice as much electric potential energy to move electrons from I to f in one coulomb.
The equation for electric potential energy is:
E=qV = E/q * Coulombs * Volts where V is voltage in volts and q is charge in Coulombs [A unit measure that equals how many charges are carried by a current]. Potential Energy can be used when considering heat generated due to resistors connected under an applied current, which would indicate that if there were two different resistors with unequal resistance (such as R and R) they have unequal amounts of electrical potential energy-thus producing more heat on the side with higher resistance.
The potential energy in an electric field is also known as the voltage. Voltage, or electrical potential difference, can be defined as a measure of how much work will need to be done by charges on one side of an equilibrium line for them to reach the other side and achieve balance (or neutrality). This article discusses a mathematical equation that measures this type of potential energy called Joules.
As electrons move from I to f they are decreasing their Electric Potential Energy because they have less movement needed in order to make up any differences between points i and f. The total amount of charge q moving through a wire creates more heat but with resistors R being lower it will take twice as long for half the number of coulombs created by the charge, q to produce a voltage drop.
E = -∫VdQ\, or E= ∫qVdr
Where V(r) is the voltage as an example of potential difference and Q(s) represents the total amount of charge on either side of equilibrium liner with a positive sign representing one side and a negative sign representing the other. Electric Potential Energy decreases linearly from I to f because there are fewer coulombs created by resistors R being lower which make up any differences between points i and f. With this in mind, it can be concluded that more work would need to be done than what was originally calculated since tighter resistors require more time before they generate the same amount of voltage.
F = q(V I – V f)\\
E=∫qVdr or E=- ∮Q dr\, since r is greater than zero and the direction of charge flow is from high potential to low potential (pointing outwards). For this equation, we will use F since it’s easier so that work can be done on a graph rather than in the equation. The electric field lines are density gradients for charges with a gradient pointing towards point I which means an increase in positive charge at point I and a negative charge at point f. This causes more electrons to travel from the left side to right because these electrons want to reach equilibrium levels by traveling downwards along electric field lines in order to reach a more stable environment. This is why they are flowing from the point I to f and as the electric potential energy changes, so do their speed of travel and amount of voltage generated because it takes more time for them to generate the same amount of voltage.