DC circuits: series and parallel resistance with worked answers
Sketch the current paths before calculating resistance. Components are in series when the same current must pass through them one after the other. Parallel components connect across the same two junctions and therefore have the same potential difference.
Choose the method
For series resistors, R = R₁ + R₂. The same current passes through each resistor; their potential differences add to the supply voltage.
For parallel resistors, 1/R = 1/R₁ + 1/R₂. Branch currents add to the supply current. The equivalent resistance is smaller than the smallest branch resistance.
Use V = IR for the particular resistor or combination in question. An ideal ammeter goes in series; an ideal voltmeter goes in parallel across the component being measured.
Worked examples
Example 1
A 6.0 V ideal supply is connected to 2.0 Ω and 4.0 Ω resistors in series. Find the current and the voltage across the 4.0 Ω resistor.
Total resistance = 2.0 + 4.0 = 6.0 Ω.
Current = 6.0/6.0 = 1.0 A throughout the series circuit.
Voltage across 4.0 Ω = 1.0 × 4.0 = 4.0 V. The other resistor has 2.0 V, giving 6.0 V in total.
Example 2
The same 2.0 Ω and 4.0 Ω resistors are placed in parallel across 6.0 V. Find the supply current.
Each branch has 6.0 V. Branch currents are 6.0/2.0 = 3.0 A and 6.0/4.0 = 1.5 A.
Supply current = 3.0 + 1.5 = 4.5 A.
Equivalent resistance = 6.0/4.5 = 1.33 Ω to 3 significant figures, smaller than 2.0 Ω.
Try it yourself
A 3.0 Ω resistor carries 2.0 A for 10 s. Find the energy transferred.
Show the worked answer
Power = I²R = 2.0² × 3.0 = 12 W.
Energy = Pt = 12 × 10 = 120 J.
Common mistakes
A voltage labelled on the supply is not automatically the voltage across one series resistor.
Use the reciprocal sum for parallel resistance, not the ordinary sum.
Sources and review
SEAB 2026 syllabus: 2026 Combined Science physics component: current and DC circuits; also useful for Pure Physics revision.
Original Rae practice, prepared with AI assistance. Selected numerical results and their displayed working are automatically checked at publication; this does not verify every explanation. Curriculum references checked on 5 September 2026. No teacher review or SEAB endorsement is claimed.
What the syllabus expects
Draw circuit diagrams using power sources (cell, battery, d.c. supply or a.c. supply), switches, lamps, fixed and variable resistors, a variable potential divider (potentiometer), fuses, ammeters and voltmeters, bells, light-dependent resistors, thermistors and light-emitting diodes.
State that current is identical at every point in a series circuit and apply this in unfamiliar situations or problem solving.
State that in a series circuit the potential differences add up to the p.d. across the whole circuit and apply this in unfamiliar situations or problem solving.
State that in a parallel circuit the branch currents add up to the source current and apply this in unfamiliar situations or problem solving.
State that the p.d. is the same across each parallel branch and apply this in unfamiliar situations or problem solving.
Recall and use the formulae for the combined resistance of resistors in series and in parallel in unfamiliar situations or problem solving.
For calculations spanning a whole circuit, bring together the appropriate relationships - R = V / I among them - plus those covering current, potential difference and resistors set up in series and in parallel.
Describe how a variable potential divider (potentiometer) works.
Describe how NTC (negative temperature coefficient) thermistors and light-dependent resistors respond, and account for their role as input transducers within potential dividers.
Solve simple circuit problems that involve NTC thermistors and light-dependent resistors.
How it's examined
Questions on this topic most often ask you to determine. About 4% of the past-paper style questions in Rae's bank for this subject sit in this topic.
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