Trystan Casey
Electric potential, also known as voltage, is the potential energy per unit charge. It is the difference in potential energy of a charge moved from one point to another, divided by the charge. The electric potential difference between the two terminals of a battery is given by the amount of work done to separate opposite charges in the battery and the amount of charge separated. This potential difference is called the electromotive force of the battery. The positive terminal is at a higher voltage than the negative terminal. The electric potential energy of a battery decreases with each electron it pushes out. The change in potential energy for the battery is negative since it loses energy.
| Characteristics | Values |
|---|---|
| Electric potential | Potential energy per unit charge |
| Electric potential difference | Change in potential of a charge moved from one point to another |
| Voltage | Common name for electric potential difference |
| Electromotive force | Potential difference between the terminals of a battery |
| Energy output | Calculated by multiplying the charge moved by the potential difference |
| Electric potential energy | Cannot be calculated with the standard potential energy formula |
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What You'll Learn
Electric potential difference
Electric potential is the potential energy per unit charge. It is important to note that electric potential and electric potential energy are not the same things. Electric potential energy cannot be calculated with the standard potential energy formula, E=mgh.
The electric potential difference between the two terminals of a battery is given by the amount of work done to separate opposite charges in the battery and the amount of charge separated. The positive terminal is at a higher voltage than the negative terminal. The electric potential difference is measured in volts, and the unit of one volt, V, is equal to one joule per coulomb, J/C.
The voltage of a battery is the potential difference between its two terminals. Voltage is related to energy, but they are not the same. The energy supplied by a battery can be calculated, but as the battery discharges, some of its energy is used internally, and its terminal voltage drops.
To calculate the electric potential at any point due to a single point charge, we use the formula: Electric potential = Electric potential energy / Charge.
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Potential energy per unit charge
Electric potential is defined as the potential energy per unit charge. The unit of electric potential is the volt, which is defined as one joule per coulomb. The electric potential between two points is the change in potential energy of a charge moved from one point to another, divided by the charge.
On a macroscopic scale, the energy per electron is very small, only a tiny fraction of a joule. However, on a submicroscopic scale, this energy per particle can be significant. For example, a tiny fraction of a joule can be enough for these particles to destroy organic molecules and harm living tissue.
It is useful to have an energy unit related to submicroscopic effects. For example, an electron accelerated between two charged metal plates is given kinetic energy that can be converted into another form, such as light in a television tube. On the submicroscopic scale, it is more convenient to define an energy unit called the electron volt (eV), which is the energy given to a fundamental charge accelerated through a potential difference of 1 V.
The relationship between potential difference (or voltage) and electrical potential energy is given by the equation:
\[ \Delta V = \frac{\Delta PE}{q} \]
Where \(\Delta V\) is the potential difference, \(\Delta PE\) is the change in potential energy, and \(q\) is the charge. Voltage is not the same as energy; it is the energy per unit charge. For example, a motorcycle battery and a car battery can both have the same voltage, but one can store much more energy than the other since \(\Delta PE = q \Delta V\).
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Voltage and energy
The electric potential across a battery is the potential difference between its two terminals. It is calculated as the potential energy per unit charge. The potential difference is the voltage, which is a measure of the energy transferred per unit of charge passed. Voltage is measured in volts (V), where 1 volt is equivalent to 1 joule of energy per coulomb.
The relationship between voltage and energy can be understood by considering the analogy of water flow and electrical current. Voltage is referred to as "electrical pressure", similar to how height corresponds to pressure in water flow. In this analogy, height corresponds to voltage, and mass corresponds to charge. There are two types of energy: kinetic energy, or energy in motion, and potential energy, or energy by virtue of position. Potential energy is calculated as the product of mass, gravity, and height, or $w = mgh$.
The electric potential across a battery can be calculated using the equation $\Delta U = q \Delta V$, where $\Delta U$ is the change in potential energy, q is the charge, and $\Delta V$ is the change in voltage. For example, when a 12.0-V car battery powers a 30.0-W headlight, the charge moved is related to voltage and energy through this equation.
It is important to note that voltage and energy are not the same. While voltage refers to the potential difference between two points, energy refers to the amount of energy transferred or the potential energy of an object. For instance, a motorcycle battery and a car battery can have the same voltage but differ in the amount of energy they store. Similarly, a high voltage with a low charge and energy may not be lethal, but the same voltage with a higher charge and energy could be dangerous.
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Work done to separate charges
The work done to separate charges in a battery is a fundamental concept in understanding how batteries function. This process is facilitated by chemical reactions within the battery, where electrons are added to the anode, making it negative, while they are simultaneously removed from the cathode, making it positive. This results in a voltage difference between the battery terminals.
The energy required to transport a unit charge from one location in the electric field to another is quantified by the electric potential, also known as the electromotive force (EMF). The volt (V) is the unit of electric potential and represents the work done per unit charge. The higher the EMF of a battery, the greater the work it can perform per unit charge, and the longer it can go without needing to be recharged.
The chemical reactions in a battery involve the flow of electrons from one material (electrode) to another, through an external circuit, which creates an electric current. To balance the flow of electrons, charged ions also flow through an electrolyte solution that is in contact with both electrodes. The electrolyte provides a pathway for the transfer of positively charged ions, which is necessary to balance the negative flow of electrons and maintain a neutral charge balance on the electrodes.
The work done to separate charges in a battery is essentially the conversion of chemical potential energy into electrical energy. When electrons move from the cathode to the anode during the charging process, they increase the chemical potential energy, thus charging the battery. Conversely, when they move in the opposite direction during the discharging process, they convert this stored chemical potential energy into electricity in the circuit, thereby discharging the battery.
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Battery voltage and energy supplied
The electric potential, or voltage, of a battery is the potential difference between its two terminals. The positive terminal is the cathode, and the negative terminal is the anode. The negative terminal has an excess of negative charge, which is repelled and attracted to the excess positive charge on the positive terminal. This movement of charge creates an electric current.
The energy supplied by a battery can be calculated using the equation $E=VIt$, where $I$ is the current through the battery. The voltage of a battery is not the same as its energy. Voltage is the energy per unit charge, so two batteries can have the same voltage but differ in the amount of energy they store. The energy stored in a battery is known as its power capacity, which is often expressed in Watt-hours (Wh). This can be calculated by multiplying the voltage of the battery by the current it can supply, usually in hours. This is represented by the equation: Voltage * Amps * hours = Wh.
The power capability of a battery, or how much current can be drawn from it, is measured in C's. A C is the Amp-hour capacity divided by 1 hour. So, the C of a 2Ah battery is 2A. The higher the C, the more current can be drawn from the battery without exhausting it.
It is important to note that as a battery is discharged, some of its energy is used internally, and its terminal voltage drops. This means that not all of the energy is available for external use.
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Frequently asked questions
Electric potential is the electric potential energy per unit charge. The SI unit of electric potential is the volt (V).
Electric potential is a scalar quantity as it has no direction, whereas electric potential energy has a direction and is measured in joules (J).
The electric potential difference between two points, A and B, is defined as the work done to move a positive unit charge from A to B. The SI unit of potential difference is volt (V).
The electric potential difference across a battery is the potential difference between its two terminals. It is calculated as the work done to separate opposite charges in the battery, divided by the amount of charge separated.
The electric potential at a point P due to a charge q is inversely proportional to the distance between them. The electric potential at any point can be defined as the amount of work done in moving a test charge from infinity to that point.
