1. Find the equivalent of 4 Ω and 12 Ω in parallel.
- 1/R=1/4+1/12=4/12=1/3.
- R=3 Ω.
- It is below 4 Ω, the smaller branch, as expected.
Science · Suggested Class 10 · school sequences vary
Series & Parallel Resistance: Class 10 Circuit Examples
The same 3 Ω and 6 Ω resistors can behave like 9 Ω—or like 2 Ω. The difference is the junctions, not where the symbols sit on the page.
Start here
Series resistances add and carry the same current. Parallel branches share voltage and add conductances: 1/R = 1/R₁ + 1/R₂ + … .
Original BananaLearn guide · 7 November 2026
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Identify the connection before calculating
Resistors are in series when they share a current path without a branching junction between them. In parallel, their endpoints connect to the same pair of circuit nodes. Trace the wires and label the nodes first.
Two symbols drawn beside each other need not be series. Wires may bend or be redrawn without changing which nodes connect. This guide uses ideal wires, an ideal supply and fixed ohmic resistors.
Derive the series rule
For two series resistors, the current I is the same through both. Their voltage drops are V₁=IR₁ and V₂=IR₂. The total supply drop is I(R₁+R₂), so the equivalent resistance is R₁+R₂.
The current is not “used up” by the first resistor. Energy is transferred, while charge flows through the complete circuit. Individual voltage drops need not be equal unless the resistances are equal.
Derive the parallel rule
Parallel branches share the same voltage V. Their currents are I₁=V/R₁ and I₂=V/R₂, and the total current is their sum. Therefore I=V(1/R₁+1/R₂), giving 1/R=1/R₁+1/R₂.
For two resistors this simplifies to R=R₁R₂/(R₁+R₂). Do not use that two-resistor shortcut unaltered for three branches. Add the reciprocals or combine one stage at a time.
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Use a size check before the final answer
A series equivalent of positive resistances is greater than any individual resistor. A parallel equivalent is smaller than the smallest branch resistance.
If 3 Ω and 6 Ω in parallel produce 9 Ω in your work, the size check reveals a connection or formula error. It does not replace the calculation, but it is an independent way to catch one.
Calculate branch currents and voltage drops
Across a 6 V supply, separate 3 Ω and 6 Ω parallel branches carry 2 A and 1 A. The total is 3 A, consistent with the 2 Ω equivalent.
If the same resistors are series across 6 V, the total resistance is 9 Ω and current is 2/3 A. Voltage drops are 2 V and 4 V, adding to 6 V. State the circuit before reusing any of those values.
Simplify a mixed circuit in stages
If a 2 Ω resistor is in series with the parallel combination of 3 Ω and 6 Ω, first replace the parallel part by 2 Ω. The whole circuit is then 2+2=4 Ω.
Across 12 V, total current is 3 A. The series 2 Ω resistor drops 6 V, leaving 6 V across the parallel section. The branch currents 2 A and 1 A add back to 3 A.
Do not confuse an open branch with a short circuit
An open branch interrupts that path; in a simple parallel network other intact branches can still carry current. An ideal zero-resistance bypass across a resistor is a short circuit and changes the network differently.
These are circuit reasoning examples, not instructions to modify equipment. Use the supplied diagrams and numbers; do not experiment with mains electricity or deliberately short a cell.
Complete a circuit checking record
Record the two nodes for each parallel section, reduce one stage at a time, apply V=IR and verify current conservation at junctions and voltage sums around the chosen path. Include units at every final value.
Parents can ask which quantity is shared—current or voltage—before asking for a formula. This guide covers reducible series/parallel combinations; not every bridge network can be simplified by visual pair grouping alone.
See the reasoning
Worked examples and checks
2. Two 5 Ω resistors are series across 10 V. Find current and drops.
- Total R=10 Ω, so I=10/10=1 A.
- Each drop is 1×5=5 V.
- The drops sum to the supply and the same current passes both.
3. A 2 Ω resistor is series with 3 Ω || 6 Ω across 12 V.
- Parallel equivalent=2 Ω; total=4 Ω. Total current=3 A.
- Series drop=6 V, leaving 6 V across each parallel branch.
- Branch currents are 2 A and 1 A; their sum equals the total.
Try, explain, check
12 questions with explained answers
Try each task before opening its explanation. These are original BananaLearn questions, not official exam or past-paper questions. Where several answers can work, the explanation gives the criteria.
Find 2 Ω+7 Ω in series.
Check answer and reasoning
9 Ω
Series resistances add.Find 4 Ω||4 Ω.
Check answer and reasoning
2 Ω
Two equal parallel resistors give half one resistance.Find 3 Ω||6 Ω.
Check answer and reasoning
2 Ω
18/9=2.Which quantity is equal in parallel branches?
Check answer and reasoning
Voltage
They share the same pair of nodes.Which quantity is equal through series elements?
Check answer and reasoning
Current
There is no branching between them.A 12 Ω equivalent is claimed for 3 Ω||6 Ω. Is it plausible?
Check answer and reasoning
No
A parallel equivalent must be below 3 Ω here.Find current through 6 Ω across 12 V.
Check answer and reasoning
2 A
I=V/R.Find the drop across 4 Ω carrying 0.5 A.
Check answer and reasoning
2 V
V=IR.Find the equivalent of three 6 Ω parallel branches.
Check answer and reasoning
2 Ω
1/R=3/6=1/2.Does a resistor use up current so the next series resistor receives less?
Check answer and reasoning
No
In a steady series path the same charge flow passes both.Can wire shape alone determine series versus parallel?
Check answer and reasoning
No
Node connections determine the relationship.What independent checks can you use in a mixed circuit?
Check answer and reasoning
Branch currents sum at a junction; voltage drops match the supply path
Also check the equivalent resistance is sensible.
A checking record to use in your notebook
Copy these headings and fill them for one worked task, then for a fresh attempt. Use your own evidence rather than copying the model answer.
- Question or sentence
- What am I being asked to explain?
- Model or evidence
- Which diagram, rule or passage detail supports my method?
- Work
- What steps connect the question to the answer?
- Independent check
- Can I substitute, recount, trace a path or check the text?
- Next attempt
- What changes in a fresh example?
Choose the next useful step
- Use voltage, current and resistance
- Revisit complete circuit paths
- Practise formula substitution and units
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Original BananaLearn explanations, examples, illustrations and practice. Source facts checked 7 November 2026. Suggested levels are learning guides, not a claim that every board or textbook uses the same sequence.
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