Current, Potential Difference and Circuit Analysis
Current, Potential Difference and Circuit Analysis
Lesson duration is: 50 minItems in this lesson
Current, Potential Difference and Circuit Analysis
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Learning objective
I can analyse series, parallel and potential-divider circuits using current, potential difference and conservation laws.
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What words do you link with current and potential difference?
Use this to activate prior knowledge and surface misconceptions such as 'current is used up' or 'voltage flows'. Invite students to explain one word they submitted.
Lesson overview
This KS5 physics lesson explores Current, Potential Difference and Circuit Analysis. Students apply conservation laws, resistivity and component characteristics to analyse series, parallel and potential-divider circuits. It is suitable for A level classroom teaching, independent study or exam revision.
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Current: what is flowing?
Current is the rate of flow of charge.
$ I = \dfrac{Q}{t} $
current is measured in amperes, A
charge is measured in coulombs, C
time is measured in seconds, s
1 A means 1 C of charge passes a point each second
Students often say current is 'used up'. Emphasise that charge is conserved: the current entering a component equals the current leaving it in a steady circuit.
Conventional current and electrons
Conventional current is defined as the direction positive charge would move
in metal wires, electrons move in the opposite direction
circuit diagrams and calculations use conventional current
Useful distinction for A level wording: current direction on diagrams is not the same as electron drift direction in a metal conductor.
Potential difference: energy transfer per coulomb
Potential difference is the energy transferred per unit charge.
$ V = \dfrac{W}{Q} $
potential difference is measured in volts, V
energy transferred is measured in joules, J
1 V means 1 J of energy transferred for each coulomb of charge
Link this to a battery or supply: the source gives energy to charges, and components transfer that energy to other forms such as thermal energy or light.
Current and potential difference are not the same
Current tells us how much charge flows each second
Potential difference tells us how much energy each coulomb transfers
a circuit can have the same current through several components but different potential differences across them
A common misconception is to treat voltage as something that flows. Clarify that charge flows; potential difference is a measure of energy transfer.
What does a current of 1 A mean?
1 C each second
1 J each second
1 V each coulomb
1 Ω each second
Checks the definition I = Q/t. Distractors mix up charge, energy and resistance units.
Complete the summary
In a steady circuit, charge is conserved, so current is not up by a component. Potential difference is the energy transferred per unit , not something that flows around the circuit.
Targets the opening conceptual distinctions: current as rate of flow of charge, and potential difference as energy transferred per coulomb.
Why is 'current is used up' wrong?
Expected elements: current is conserved at a component in a steady circuit, so the same current enters and leaves; the component transfers energy, so potential difference is linked to energy per coulomb, not loss of charge.
Conservation laws in circuits
Circuit analysis is built on two conservation ideas:
Charge is conserved → current into a junction equals current out
Energy is conserved → the total potential difference supplied equals the total potential difference across components in a complete loop
these rules apply before substituting values into equations
This is the conceptual bridge into series and parallel circuits. Students should see Kirchhoff-style rules as conservation laws, not isolated facts to memorise.
Series circuits
In a series circuit there is one path for charge flow.
the current is the same through every component
the potential differences add up to the supply potential difference
the total resistance is the sum of the resistances
adding more components increases total resistance
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Parallel circuits
In a parallel circuit there are separate branches.
the potential difference is the same across each branch
the current splits between branches
the total current from the source is the sum of the branch currents
adding a branch reduces the total resistance
Students often reverse the series/parallel rules. Stress the path idea: one path gives same current; shared branches give same potential difference across each branch.
Using conservation to solve circuits
A reliable approach is:
identify series sections and parallel branches
apply the current rule at junctions
apply the potential difference rule around loops
use $V = IR$ for individual components or sections
check that your answers are physically consistent
The final check matters: branch currents should add correctly, and potential differences should match the supply where expected.
In a parallel circuit, what is the same across each branch?
Resistance
Current
Potential difference
Charge flow path
Tests the core series/parallel contrast. Common error is to swap current and potential difference rules.
Complete the method
To analyse a circuit, first identify series sections and parallel . Then apply the current rule at and the potential difference rule around before using V = IR.
Reinforces the structured method slide and the conservation-law language used in circuit analysis.
Resistance and Ohm's law
For an ohmic conductor at constant temperature:
$ V = IR $
resistance is measured in ohms, $\Omega$
a larger resistance gives a smaller current for the same potential difference
the equation links current, potential difference and resistance during circuit analysis
Remind students that Ohm's law in the strict sense applies when current is directly proportional to potential difference, typically at constant temperature.
What sets the resistance of a wire?
Resistance depends on both geometry and material.
$ R = \rho \dfrac{L}{A} $
$\rho$ is the resistivity of the material
longer wires have greater resistance
larger cross-sectional area gives smaller resistance
materials with high resistivity oppose charge flow more strongly
Students may confuse resistance and resistivity. Resistance belongs to a component; resistivity is a material property.
Resistivity in context
copper has low resistivity, so it is useful for connecting wires
filament materials have higher resistivity, helping energy transfer by heating
changing the wire length or area changes resistance even if the material stays the same
If useful, mention that temperature can also change resistance, especially in metal conductors, but keep the main focus on the resistivity equation.
Current–potential difference characteristics
Not all components behave like fixed resistors.
an ohmic conductor gives a straight-line I–V graph through the origin at constant temperature
a filament lamp is non-ohmic because heating increases resistance
a diode conducts easily in one direction but very little in the reverse direction
Students should recognise that using V = IR remains valid for a component at a particular operating point, even when resistance is not constant overall.
Why component characteristics matter
Component characteristics affect circuit behaviour.
a filament lamp does not have constant resistance
a diode can control current direction
a fixed resistor is often used when predictable behaviour is needed
This sets up why realistic circuit analysis must consider the type of component, not only the numbers in a formula.
If wire length doubles and material and area stay the same, resistance is
Halved
Doubled
Unchanged
Quadrupled
Uses R = ρL/A. A common misconception is to think length has no effect if the material is unchanged.
Complete the paragraph
An ohmic conductor gives a I–V graph through the origin at constant temperature. A filament lamp is because heating changes its resistance. A diode conducts mainly in direction.
Connects graph shape to component behaviour and checks three high-value terms from this subtopic.
How is resistivity different from resistance?
Expected elements: resistance belongs to a particular component or wire; resistivity is a material property; changing length or area changes resistance even when resistivity stays the same.
Potential dividers
A potential divider uses resistors in series to share the supply potential difference.
the supply potential difference is split between the components
the larger resistance gets the larger share of the potential difference
potential dividers are used to provide a chosen output potential difference
Phrase carefully: the potential difference is not 'used up' by the first resistor; the total is shared across the series components according to resistance.
Potential divider equation
For two resistors in series:
$ V{out} = V{in} \times \dfrac{R2}{R1 + R_2} $
$V_{out}$ is taken across the chosen resistor
increasing that resistor increases its share of the supply potential difference
the equation follows from the series current being the same through both resistors
Be explicit about where Vout is measured. Students often substitute the wrong resistor into the numerator.
Variable potential dividers
replacing one resistor with a thermistor or light-dependent resistor makes the output depend on temperature or light intensity
this allows sensing and control circuits
the analysis still depends on series current and the sharing of potential difference
Keep the focus on physics reasoning rather than electronics detail. The key idea is that changing resistance changes the voltage share.
A method for circuit analysis
When analysing an unfamiliar circuit:
redraw the circuit clearly if needed
label known currents, potential differences and resistances
simplify series and parallel sections where valid
apply conservation laws before calculation
use equations only after the physical structure is clear
This is the exam-technique slide: students often rush to equations before identifying the structure of the circuit.
Worked example: series circuit
A 12 V supply is connected to two resistors of 2 $\Omega$ and 4 $\Omega$ in series.
total resistance = 6 $\Omega$
current = $12/6 = 2$ A
potential difference across 2 $\Omega$ = 4 V
potential difference across 4 $\Omega$ = 8 V
4 V + 8 V = 12 V, so the loop is consistent
This slide ties together total resistance, same current in series, and voltage sharing in proportion to resistance.
Worked example: parallel circuit
A 6 V supply is connected across two parallel resistors of 3 $\Omega$ and 6 $\Omega$.
each branch has 6 V across it
current in 3 $\Omega$ branch = 2 A
current in 6 $\Omega$ branch = 1 A
total current from the source = 3 A
Point out the contrast with the series example: now the potential difference is the same across branches, while currents differ.
Worked example: potential divider
A 9 V supply is connected across 1 k$\Omega$ and 2 k$\Omega$ in series. The output is taken across the 2 k$\Omega$ resistor.
total resistance = 3 k$\Omega$
current = $9/3000 = 3.0 \times 10^{-3}$ A
output potential difference = $I R = 6$ V
this matches $V_{out} = 9 \times 2/3 = 6$ V
Useful to show both methods: direct use of the divider equation and reasoning from current plus V = IR.
Key ideas to retain
current is the rate of flow of charge
potential difference is energy transferred per coulomb
current is conserved at junctions
energy is conserved around a complete loop
series and parallel circuits follow different current and potential difference rules
component characteristics and resistivity affect real circuit behaviour
This slide resolves the central question by pulling the rules together into one coherent model for analysis.
A potential divider gives the largest Vout across the
Smaller resistor
Larger resistor
Cell
Junction
Based on the slide stating that the larger resistance gets the larger share of the supply potential difference.
Complete the applied example
In the 12 V series example, the total resistance is Ω, so the current is A. In the 6 V parallel example, the branch currents add to a total current of A.
This is the applied task check, drawing directly on the worked examples for series and parallel analysis.
What is your first step with an unfamiliar circuit?
Expected elements: identify series/parallel structure first; label known quantities; apply conservation laws; then use V = IR or the divider equation; check physical consistency.
What is one idea from today that now feels secure?
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Which part of circuit analysis still feels hardest?
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One word for what helped you understand this lesson best
Use responses to identify which explanations or examples supported learning most effectively.
Glossary
current - the rate of flow of charge
charge - a property of matter measured in coulombs
potential difference - energy transferred per unit charge
resistance - a measure of how much a component opposes current
ohmic conductor - a component for which current is proportional to potential difference at constant temperature
resistivity - a material property linking resistance to length and cross-sectional area
series circuit - a circuit in which components are connected in a single path
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Glossary
parallel circuit - a circuit with components arranged in separate branches
junction - a point where current can split or combine
branch current - the current in one path of a parallel circuit
potential divider - a series arrangement used to produce a chosen output potential difference
filament lamp - a non-ohmic component whose resistance increases as it heats up
diode - a component that conducts mainly in one direction
cross-sectional area - the area of the wire perpendicular to the direction of current
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