5.1e Electric potential

By Sergei Frolov, Soviet Digital Electronics Museum, www.leningrad.su/museum/ - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=58205251

THE IB SAYS

Essential idea: When charges move an electric current is created.

Understandings: Potential difference

Applications and skills: Calculating work done in an electric field in both joules and electronvolts; Solving problems involving current, potential difference and charge

Data booklet equations: I = ∆ q / ∆ t ; I = nAvq

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Electrical potential and potential difference

Potential energy can be thought of the energy something has due to its position. In this case the total energy will depend on the position in an electrical field and the charge on the object. We give gravitational potential energy to objects by lifting them against a gravitational field. Similarly we give electrical charges potential by moving them against an electrical field - and when charges are released in an electric field they can do work (transfer energy) under the influence of that field.

The work done is force × distance, and the force is determined by the electrical field strength (E, which is constant in a uniform field) so an expression for the electrical potential energy is electric field strength × charge × displacement.

Electrical potential is the work done per unit charge - hence the equation above becomes potential = electric field strength × displacement

Unit: the unit for electrical potential is the joules (or energy) per coulomb (of charge). This is given the SI derived unit name of the volt. 1 volt [1V] = 1 joule per coulomb

However, the question that arises is displacement from where? Generally we define an arbitrary zero - and in electrical circuits all we care about is the difference in potential between two points in a circuit. Hence we use the term potential difference. The potential difference across an energy supply (such as a cell or a generator) will be the joules per coulomb of charge input to the circuit and the potential difference across the load represents the joules per unit charge supplied to those components. Ideally there will be no potential difference across the wires / cables.

Electrical field strength and electric potential: Mathematically, electrical field strength is equal to the potential gradient (E = ∆V/d). So, for example a uniform 10NC^-1 field will have a gradient of 10Vm^-1 across the field.

The electronvolt

An electronvolt is a unit of energy arising from the equation for electrical potential energy. Electrical potential energy = charge × potential. If you use this equation with a charge measured in coulombs and a potential measured in volts then your energy is measured in joules. However, in some circumstances (particularly in particle physics) it makes more sense to use a measurement of charge equal to the elementary charge. This is the charge on an electron (or a proton) with a value of 1.6 × 10^-19 C. Every charge in the universe outside a nucleus has a value which is a multiple of this charge. If you use this as your unit for charge then you calculate the energy is units of electronvolts (eV). One electronvolt is equivalent to 1.6 × 10^-19 J.

EMF and circuits

As we said earlier, the potential difference across a supply represents energy (per unit charge) provided to the circuit, the potential difference across a load represents energy (per unit charge) taken from a circuit. In reality all supplies provide energy AND use some energy as the electricity passes through them. In other words, some of the energy they supply is "wasted" in heating the supply. The energy delivered by the supply per unit charge is referred to as the EMF. This does not include the energy used by the supply. As the EMF is a label for a particular potential difference the units are the same: volts. Since all supplies use some energy (this is known as internal resistance and we will look at it in more detail later) then the EMF is also used to describe the theoretical maximum energy provided by the supply. A new cell may be labelled as having an EMF of 1.5V, but in actual use (when a current is flowing) then some energy will be lost to the internal resistance and the potential difference across the cell (and available to the rest of the circuit) will be less than 1.5V.

EMF stands for "electromotive force", but this can be confusing - it is not a force although it is needed for a current to occur. I recommend just thinking of it and labelling it as EMF.

Circuits and power

Power is the rate of doing work, or transferring energy. The relevant equation is P = E/∆t. The SI derived unit of power is the Watt [W]. 1W = 1Js^-1 . Since potential difference is J/C and current C/s, it follows that the product of potential difference and current has units of J/s or Js^-1 .

Thus, the rate of energy transfer, or power, in one part of a circuit is equal to the product of the current in that part of the circuit multiplied by the potential difference across that part of the circuit, or P =VI.

Since V= IR, we can also write this equation in the forms P = V² / R and P = I²R.

Resources from textbooks

Oxford Physics: pages 186 - 191 again, lots of detail including worked examples

Hamper HL (2014): pages 215 - 217 for potential, page 224 on EMF and terminal pd, pages 226 - 229 on power (<--- good explanations)

Relevant questions from Dot Point Physics (5 Electric currents)

pages 225 - 230

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