Series and Parallel Circuits Practice

Total resistance, voltage and current division, and what happens when a branch opens — with circuit diagrams to read rather than descriptions to imagine.

Practise Series / Parallel

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What it is, and why electricians need it

A series circuit offers one path, so the same current flows through every component and the supply voltage divides among them. A parallel circuit offers several paths from the same two nodes, so every branch sees the full supply voltage and the branch currents add. Nearly everything else follows from those two sentences.

Building wiring is parallel, and understanding why makes circuit loading obvious rather than something to memorise. Each receptacle is its own branch across the same two conductors, so every one gets 120 volts whatever else is plugged in, and the total current the breaker sees is the sum of what each branch draws. Add a branch and the combined resistance falls, so the total current rises — which is precisely how a circuit becomes overloaded without any existing load changing.

Series connection appears in different places: a switch in series with its load, a fuse in series with the circuit it protects, control contacts in series along a ladder rung. The characteristic that makes it useful there is the same one that makes it unsuitable for lighting — an open anywhere stops everything. That is also why the Code generally prohibits a switch or an overcurrent device in a grounded conductor: opening the neutral alone would leave equipment connected to an energized conductor while appearing dead.

Combination networks are what the exam actually tends to ask about, and they yield to one discipline: reduce from the inside out. Collapse each parallel group to a single equivalent resistance first, then add the series elements. Trying to do it in one step is where candidates go wrong.

Formulas and principles

  • Rt = R1 + R2 + ... + Rn

    Series resistance. Resistances simply add.

    The total is always larger than the largest individual resistance.

  • 1 ÷ Rt = 1 ÷ R1 + 1 ÷ R2 + ... + 1 ÷ Rn

    Parallel resistance, any number of branches. Add the reciprocals, then invert.

    The total is always smaller than the smallest individual branch.

  • Rt = (R1 × R2) ÷ (R1 + R2)

    Product over sum. A shortcut for exactly two parallel branches.

    Faster and less error-prone than reciprocals when there are only two.

  • Rt = R ÷ N

    N equal resistances of value R in parallel.

    Three 60-ohm branches give 20 ohms.

  • Vout = Vin × R2 ÷ (R1 + R2)

    Voltage divider. The share taken by R2 in a series pair.

    Saves finding the circuit current first.

  • I1 = It × R2 ÷ (R1 + R2)

    Current divider for two parallel branches. Note the opposite resistance on top.

    The lower-resistance branch takes the larger share of the current.

Now try it on 16 questions

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Start the Series / Parallel drill

Worked examples

Scenario: A 10-ohm resistance is in series with two 20-ohm resistances that are in parallel with each other, supplied at 100 volts. Find the total resistance and the supply current.

  1. Reduce the innermost group first: two equal 20-ohm branches in parallel give 20 ÷ 2 = 10 ohms.
  2. That 10 ohms is now in series with the other 10 ohms.
  3. Rt = 10 + 10 = 20 ohms.
  4. I = V ÷ Rt = 100 ÷ 20 = 5 amperes.
  5. Check: the 10-ohm series element drops 5 × 10 = 50 V, leaving 50 V across the parallel pair, which at 10 ohms equivalent also draws 5 A. Consistent.

Answer: 20 ohms total, 5 amperes from the supply

Scenario: Two parallel loads of 20 ohms and 30 ohms operate on 120 volts. Find the total current two different ways, as a check.

  1. Branch by branch: 120 ÷ 20 = 6 A and 120 ÷ 30 = 4 A, so 10 A total.
  2. Or combine first: Rt = (20 × 30) ÷ 50 = 600 ÷ 50 = 12 ohms.
  3. Then I = 120 ÷ 12 = 10 A.
  4. Both routes agree, and 12 ohms is correctly smaller than the 20-ohm branch.

Answer: 10 amperes total, from a 12-ohm equivalent resistance

Common mistakes

  • Adding parallel resistances as though they were in series. Three 20-ohm branches in parallel are 6.67 ohms, not 60. The sanity check is that a parallel total must come out below the smallest branch.
  • Forgetting to invert after summing the reciprocals. Adding 1/10 + 1/15 gives 0.1667, which is the reciprocal of the answer. The resistance is 1 ÷ 0.1667 = 6 ohms.
  • Putting the same resistance on top in the current divider rule. The opposite branch resistance goes in the numerator, because the lower-resistance path takes the larger current. Getting this backwards gives you the other branch's current.
  • Reducing a combination circuit from the outside in. Always collapse the innermost parallel group first, then work outward. Mixing the order is the main source of error on combination networks.
  • Assuming a parallel branch failing open affects the others. It does not. The remaining branches keep the full supply voltage and operate normally; only the total current falls.

Related practice topics

Topics that come up alongside this one on the exam.

Questions about this topic

How do I tell a series circuit from a parallel circuit on a diagram?

Trace the current. If there is exactly one path from source to load and back, it is series. If the path divides at a junction and rejoins later, those divided branches are parallel. A combination circuit has both, and the way to handle it is to collapse the innermost parallel group first, then add the series elements.

Why does adding a parallel branch lower total resistance?

Because you have given current an extra route. The combined resistance of a parallel group is always lower than its smallest branch, which is a useful sanity check: if your parallel answer comes out larger than any individual branch, you have made an arithmetic error. At a fixed supply voltage, lower resistance means more total current, which is exactly the mechanism of an overloaded circuit.

Which quantity stays the same in each kind of circuit?

Current is the same everywhere in a series circuit, because there is one path. Voltage is the same across every branch of a parallel circuit, because all branches connect to the same two nodes. In both cases power adds: total power is the sum of the individual powers regardless of how the circuit is arranged.

Why is building wiring parallel rather than series?

Two reasons. Every outlet gets the full supply voltage regardless of what else is connected, and a failure in one branch does not interrupt the others. A series-wired lighting circuit would dim every lamp as you added more, and a single open lamp would extinguish the lot.

When do I use the voltage divider and current divider rules?

The voltage divider rule saves you from first finding the circuit current: each series element takes a share of the supply equal to its own resistance over the total. The current divider rule does the same for a two-branch parallel group, except the opposite branch resistance goes on top, because the lower-resistance path takes the larger share.

How does this show up on the licensing exam?

Usually as total resistance or total current in a small network, often with a diagram, and sometimes as a reasoning question about what happens when a branch opens. It also underpins the practical questions: a branch circuit is a parallel network, so understanding why adding loads raises current is what makes circuit loading intuitive rather than memorised.

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