Potential difference, current and resistance IB DP Physics Study Notes - 2025 Syllabus

Potential difference, current and resistance IB DP Physics Study Notes

Potential difference, current and resistance IB DP Physics Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

that cells provide a source of emf
chemical cells and solar cells as the energy source in circuits
that circuit diagrams represent the arrangement of components in a circuit
direct current (dc) $I$ as a flow of charge carriers as given by $I = \frac{\Delta q}{\Delta t}$
that the electric potential difference $V$ is the work done per unit charge on moving a positive charge between two points along the path of the current as given by $V = \frac{W}{q}$
the properties of electrical conductors and insulators in terms of mobility of charge carriers
electric resistance and its origin
electrical resistance $R$ as given by $R = \frac{V}{I}$
resistivity as given by $\rho = \frac{RA}{L}$

Standard level and higher level: There is no Standard level content
Additional higher level: 8 hours

IB DP Physics 2025 -Study Notes -All Topics

Cells – electromotive force (emf)

∙The electromotive force ε (or emf) of a cell is the amount of chemical energy converted to electrical energy per unit charge.
∙Since energy per unit charge is volts, emf is measured in volts.
∙This cell has an emf of ε = 1.6 V.
∙Because the cell is not connected to any circuit we say that it is unloaded

EXAMPLE:

How much chemical energy is converted to electrical energy by the cell if a charge of 15 µC is drawn by the voltmeter?

▶️Answer/Explanation

SOLUTION:

• From ΔV = ΔEp/q
we have ε = ΔEp/q

• Thus
ΔEp = εq
= (1.6)(15×10⁻⁶)
= 2.4×10⁻⁵ J.

Photovoltaic cells

∙The photovoltaic cell converts sunlight directly into electricity.
∙The cell is made of crystalline silicon (a semiconductor) doped with phosphorus and boron impurities.

∙Like a chemical cell, a photovoltaic cell also produces a steady flow of electrons for current
∙The downside to a photovoltaic cell is that how many electrons you can get (and thus it’s power output) is determined by how much sunlight is hitting it.
less sunlight = less power
This means that the power output is dependent on things like weather (clouds), time of day (night), and in some places, the season (winter vs. summer).

Electric circuits

∙An electric circuit is a set of conductors (like wires) and components (like resistors, lights, etc.) connected to an electrical voltage source (like a cell or a battery) in such a way that current can flow in complete loops.
∙Here are two circuits consisting of cells, resistors, and wires.
∙Note current flowing from (+) to (-) in each circuit.

A complete circuit will always contain a cell or a battery.
∙The schematic diagram of a cell is this:

∙A battery is just a group of cells connected in series:

∙If each cell is 1.5 V, then the battery above is 3(1.5) = 4.5 V. What is the voltage of your calculator battery?
∙A fixed-value resistor looks like this:

∙The schematic of a fixed-value resistor looks like this:

EXAMPLE:

Draw schematic diagrams of each of the following circuits:

▶️Answer/Explanation

Solution:

Cells

∙To make a chemical cell, or a battery, you can begin with a container of weak acid, and two electrodes made of different metals.
∙Different metals dissolve in acids at different rates.
∙When a metal dissolves, it enters the acid as a positive ion, leaving behind an electron.
∙We call the weak acid the electrolyte. We call the least negative metal the positive terminal. We call the most negative metal the negative terminal.

∙Think of a chemical cell as a device that converts chemical energy into electrical energy.
∙If we connect conductors and a light bulb to the (+) and the (-) terminals, we see that electrons begin to flow in an electric current.

FYI
∙Why do the electrons run from (-) to (+) in the external circuit instead of the reverse?

Cells – primary and secondary

∙Each time an electron leaves the (-), the acid creates another electron.
∙Each time an electron enters the (+), the acid neutralizes an electron.
∙This process is maintained until one of the metals or the electrolyte is completely used up.
∙A primary cell can’t be recharged.
∙A secondary cell can be recharged by applying an external voltage, reversing the chemical reaction.

Cells – current

PRACTICE:

A current isn’t really just one electron moving through a circuit. It is in reality more like a chain of them, each one shoving the next through the circuit. Recalling the charge law “like charges repel, and unlike charges attract,” explain why the current flows from (-) to (+) in terms of the force of repulsion.
SOLUTION:

∙Consider electrons at A and B.
∙Both electrons feel a repulsive force at their respective electrodes.

Cells – conventional current

∙Back in the days of Ben Franklin scientists understood that there were two types of electricity: positive and negative.
∙What they didn’t know was which one was actually free to travel through a circuit.
∙The influential Ben Franklin guessed wrongly that it was the positive charge.

Cells – electric potential difference

• We define the electric potential difference ΔV as the amount of work done in moving a positive charge q from a point of lower potential energy to a point of higher potential energy.

• The units for electric potential difference are volts V or, as can be seen from the formula, J C⁻¹.

FYI • Electric potential difference is often abbreviated p.d.

Think of a battery as an engine that uses chemical energy to take positive charges and move them from low to high potential within the cell so that they can do work outside the cell in the external circuit.
∙As an analogy to gravitational potential energy, think of the chemical cell as an elevator, powered by a chemical engine.
∙Inside the cell, positive charges at low potential are raised through chemical energy to high potential.
∙Outside the cell, positive charges at high potential are released into the external circuit to do their electrical work, losing energy as they go.

EXAMPLE:

200 µC of charge is brought from an electric potential of 2.0 V to an electric potential of 14 V through use of a car battery. What is the change in potential energy of the charge?¹

▶️Answer/Explanation

SOLUTION:

ΔEₚ • From ΔV = we see that ΔEₚ = qΔV. Thus

ΔEₚ = q(V-V₀)

ΔEₚ = (200×10⁻⁶)(14-2)

ΔEₚ = 0.0024 J.

Electric current

∙Electric current I is the time it takes (∆t) for a charge ∆q to move past a particular point in a circuit.

∙From the formula it should be clear that current is measured in Coulombs per second (C s^-1) which is called an Ampere (A). ∙A simple model may help clarify current flow.
∙Think of conductors as “pipes” that hold electrons.
∙The chemical cell pushes an electron out of the (-) side. This electron in turn pushes the next, and so on, because like charges repel.
∙This “electromotive force” is transfered simultaneously to every charge in the circuit.

EXAMPLE:

Explain why when a wire is cut current stops everywhere and does not “leak” into the air.

SOLUTION:

∙Freeing an e- from a conductor takes a lot of energy.
∙This is why you don’t get electrocuted by e- jumping off of nearby conductors like outlets (unless the voltage is very high).
∙This is also why when you cut the wire e- do not leak out into the surrounding environment.
∙Finally, if the chain is broken the push stops, so the current stops everywhere.

Conductors and Insulators

We can classify materials generally according to the ability of charge to move through them (What is the classification of materials according to the ability of charge moving through them or according to the conductivity?)

2.1.1 Conductors are materials through which charge can move rather freely; examples include metals (such as copper in common lamp wire), the human body, and tap water.

Free electrons are not bound to the atoms.
These electrons can move relatively freely through the material.
Examples of good conductors include copper, aluminum, and silver.
When a good conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material.

2.1.2 Insulators: Electrical insulators are materials in which all of the electrons are bound to atoms.

These electrons cannot move relatively freely through the material.
Examples of good insulators include glass, rubber, and wood.
When a good insulator is charged in a small region, the charge is unable to move to other regions of the material.

Resistance

∙If you have ever looked inside an electronic device you have no doubt seen what a resistor looks like.

∙A resistor’s working part is usually made of carbon, which is a semiconductor.
∙The less carbon there is, the harder it is for current to flow through the resistor.
∙As the animation shows, carbon is spiraled away to cut down the cross-sectional area, thereby increasing the resistance to whatever value is desired.
∙Some very precise resistors are made of wire and are called wire-wound resistors.
∙And some resistors can be made to vary their resistance by tapping them at various places. These are called variable resistors and potentiometers.
∙Thermistors are temperature- dependent resistors, changing their resistance in response to their temperature.
∙Light-dependent resistors (LDRs) change their resistance in response to light intensity.

∙Electrical resistance R is a measure of how hard it is for current to flow through a material. Resistance is measured in ohms (Ω) using an ohm-meter.

The different types of resistors have different schematic symbols.

The resistance R of a material is the ratio of the potential difference V across the material to the current I flowing through the material.

∙The units from the formula are (V A^-1) which are called ohms (Ω).

PRACTICE:

A fixed resistor has a current of 18.2 mA when it has a 6.0 V potential difference across it. What is its resistance?

SOLUTION: Last color is number of zeros.
$R = V/I = 6.0 / 18.2 x 10^-3 = 330 Ω$.

To understand electrical resistance, consider two identical milk shakes.
In the first experiment: The straws have the same diameter, but different lengths.
In the second experiment: The straws have the same length, but different diameters.
Note that $R \propto \frac{L}{A}$
Of course conductors and resistors are not hollow like straws. And instead of milk shake current we have electrical current.
Even through solids R ∝ L/A
But R also depends on the material through which the electricity is flowing.
For example the exact same size of copper will have much less resistance than the carbon.
With the proportionality constant ρ we have equality:
∙The Greek ρ is the resistivity of the particular material the resistor is made from. It is measured in Ωm.
Note that resistance depends on temperature. The IBO does not require us to explore this facet of resistivity.