Current, potential difference & circuits

Learning goals

What students should be able to explain, calculate and investigate after completing Current, Potential Difference, EMF and Circuits.

• Define electric current and relate it to the flow of charge.
• Distinguish conventional current from electron flow.
• Recognise and use standard circuit symbols, and connect ammeters/voltmeters correctly.
• Apply the current and potential-difference rules for series and parallel circuits.
• Higher Level: Derive and use the formulae for equivalent resistance in series and parallel.
• Define EMF and distinguish it from potential difference.
• Calculate energy and power in circuits.

Key definitions

Precise terms, symbols and SI units used in Current, Potential Difference, EMF and Circuits.

Current and Charge

Electric current is the rate of flow of charge: I = Q/t.

Electric current is the rate at which charge passes a point. In metals, electrons drift through a lattice, but conventional current is defined in the direction positive charge would move and is therefore opposite to electron drift. Charge is not used up by a component; energy is transferred as charge moves through it.

Circuit Components and Symbols

Circuit diagrams use standard symbols so they can be understood internationally.

An ammeter is always connected in series (so the full circuit current passes through it) and should have very low resistance so it does not affect the current it is measuring. A voltmeter is always connected in parallel across the component being measured (so it measures the potential difference across it) and should have very high resistance so it draws negligible current itself.

Series and Parallel Circuits

In a series circuit the same current flows through every component and the supply potential difference is shared; in parallel, each branch has the same potential difference and the currents in the branches add to the total current.

In a parallel circuit, the potential difference is the same across every branch (they are all connected between the same two points), and the total current supplied splits between the branches — more current flows through the branch with lower resistance.

The qualitative current and potential-difference rules are required for all students. Deriving and using the equivalent-resistance formulae for series and parallel combinations is Higher Level.

Check: a series combination has a total resistance greater than any individual resistor. A parallel combination has a total resistance smaller than the smallest branch resistance.

EMF and Potential Difference

EMF describes the total energy per unit charge supplied by a source.

EMF is energy supplied per coulomb by a source. Potential difference is energy transferred per coulomb in a component. A 12 V source supplies 12 J to each coulomb. If two series components have p.d.s of 5 V and 7 V, they transfer 5 J and 7 J per coulomb, giving 12 J per coulomb in total. Charge keeps moving around the circuit: current is not used up, and voltage does not flow.

• Source: 12 J supplied to each coulomb.
• First component: 5 J transferred from each coulomb.
• Second component: 7 J transferred from each coulomb.
• Total energy transferred = 12 J per coulomb.

Energy and Power in Circuits

Electrical power is the rate at which electrical energy is transferred: P = VI.

A potential difference of one volt means one joule is transferred per coulomb. Since current is coulombs per second, multiplying V by I gives joules per second, or power. The alternative forms I²R and V²/R follow from Ohm’s law and should be used only with the appropriate voltage, current and resistance for that component.

Diagrams and formulae

Key diagrams and equations for reviewing Current, Potential Difference, EMF and Circuits.

• Standard circuit symbols used in Leaving Certificate circuit diagrams.
• Correct meter placement: the ammeter is in series with the circuit (so all the current flows through it); the voltmeter is in parallel with the component being measured.
• Series resistors: total resistance is the simple sum. Parallel resistors: the reciprocal of the total resistance is the sum of the reciprocals, so the total resistance is always less than the smallest individual resistor.

Standard circuit symbols used in Leaving Certificate circuit diagrams.

Correct meter placement: the ammeter is in series with the circuit (so all the current flows through it); the voltmeter is in parallel with the component being measured.

Series resistors: total resistance is the simple sum. Parallel resistors: the reciprocal of the total resistance is the sum of the reciprocals, so the total resistance is always less than the smallest individual resistor.

Worked Example

A step-by-step calculation applying the central relationships in Current, Potential Difference, EMF and Circuits.

Two resistors of 4 Ω and 12 Ω are connected in parallel. Calculate the combined resistance.

• 1/R = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3
• R = 3 Ω
• (Note: the combined resistance, 3 Ω, is smaller than either individual resistor, as expected for a parallel combination.)

Practical / Investigation

Experimental planning, measurement and evaluation for Current, Potential Difference, EMF and Circuits.

Experiment: Resistors in series and parallel

• Apparatus: power supply, two or more resistors of known value, ammeter, voltmeter, connecting wires.
• Method (series): connect resistors end-to-end in a single loop with the ammeter in series; measure the current (same throughout) and the voltage across each resistor and across the whole combination.
• Method (parallel): connect resistors between the same two points; measure the voltage (same across each branch) and the current in each branch and in the main supply line.
• Verify that measured total resistance matches R = R₁+R₂+... (series) or 1/R = 1/R₁+1/R₂+... (parallel), calculated from R = V/I for the combination.
• Sources of error: resistance of connecting wires and meters is not exactly zero/infinite; component values may differ slightly from their stated (nominal) values.
• Improvement: use short, thick connecting wires; measure actual resistor values with an ohmmeter beforehand rather than trusting printed values.

• Use the ammeter in series and the voltmeter in parallel. Record component values and measured current/potential difference with units.
• For series, compare Vtotal with the sum of component voltages and calculate Rtotal = Vtotal/I. For parallel, compare Itotal with the sum of branch currents.
• Disconnect the supply while rearranging the circuit; use a low, safe voltage and avoid overheating resistors.

Quick-Check Questions

Short retrieval questions covering the essential ideas in Current, Potential Difference, EMF and Circuits.

1. Define electric current.

2. Why must an ammeter have very low resistance?

3. State the rule for current in a series circuit, and for voltage in a parallel circuit.

4. Distinguish EMF from potential difference.

5. Write the three equivalent formulas for electrical power.

Common mistakes and exam tips

Common misconceptions and exam-technique checks for Current, Potential Difference, EMF and Circuits.

• Avoid: Connecting an ammeter in parallel or a voltmeter in series. Correct idea: Connect an ammeter in series and a voltmeter in parallel with the component being measured.
• Avoid: Thinking current is used up in a series circuit. Correct idea: Charge is conserved, so the current is the same throughout a series circuit; energy is transferred in components.
• Avoid: Stopping after calculating 1/R for parallel resistors. Correct idea: Take the reciprocal to obtain the equivalent resistance R.

• Decide whether components are in series or parallel before applying current and voltage rules.
• Use conventional-current direction consistently on circuit diagrams.
• For parallel resistors, check that the equivalent resistance is less than the smallest branch resistance.

Exam-style questions

Five exam-style questions with worked answers on Current, Potential Difference, EMF and Circuits.

Higher Level — Required Content

Required Higher Level content for this topic.

The same current passes through each series resistor and the potential differences add. Substituting V = IR gives:

The potential difference is common to each branch and the branch currents add. Substituting I = V/R gives:

End-of-unit revision

Formulae, definitions, experiments and mixed revision questions for Current, Potential Difference, EMF and Circuits.

Try without notes: state where an ammeter and a voltmeter are connected, and derive the parallel-resistor formula for two resistors.

• I = Q/t
• Series: R = R₁ + R₂ + ...
• Parallel: 1/R = 1/R₁ + 1/R₂ + ...
• P = VI = I²R = V²/R
• W = VIt = I²Rt = Pt

• Current
• Conventional current vs electron flow
• EMF vs potential difference
• Series vs parallel circuits

• Standard circuit symbols
• Correct ammeter (series) and voltmeter (parallel) placement
• Series and parallel resistor networks

• Verifying the rules for resistors in series and in parallel

• Ammeter/voltmeter wrongly placed
• Forgetting to invert 1/R for parallel resistance
• Thinking current is 'used up' around a series circuit
• Confusing EMF with potential difference

1. Three resistors of 2 Ω, 3 Ω and 6 Ω are connected in parallel. Calculate the combined resistance.

2. A 12 V supply drives a current of 2 A through a resistor for 30 s. Calculate the energy transferred.

3. Explain why a voltmeter must have a very high resistance.

4. Two identical bulbs are connected in parallel across a battery. Compare the brightness of the bulbs to the case where they are connected in series across the same battery.

1. 1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1 → R = 1 Ω.

2. W = VIt = 12 × 2 × 30 = 720 J.

3. A voltmeter is connected in parallel across a component; if its resistance were low, it would draw significant current itself and alter the very circuit it is trying to measure, so a very high resistance keeps its effect on the circuit negligible.

4. In parallel, each bulb gets the full supply voltage, so both glow at normal (full) brightness; in series, the supply voltage is shared between the two bulbs, so each gets less voltage and glows more dimly than in the parallel case.

The table below shows which equations from this unit appear in the official State Examinations Commission Formulae and Tables book, and where.