Electricity and Circuit Foundations
Series, Parallel, Open and Short Circuits
See how connections change current and voltage pathways.
A real system shows a symptom related to “Series, Parallel, Open and Short Circuits”, and you need to find the cause before replacing parts or changing settings.
Use nodes and paths to identify true series and parallel connections, calculate simple resistive networks, and distinguish an interrupted circuit from a low-impedance fault path.
- Select or check first
- Trace nodes before writing equations. An ideal wire joins points into one node, even if it bends around the drawing. Redrawing the same node arrangement does not change the circuit. Mark nodes and branches first; then decide which current is shared, which voltage is shared and whether a series-parallel reduction is valid.
- Controlling assumption
- Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
- Top risk
- An open can still hold dangerous voltage; a short can release dangerous energy. Never touch an open conductor because branch current appears absent, and never create a short as a test. Stored-energy and generation sources can maintain or restore voltage.
- Proof
- Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Start with the basics Optional foundation before “Series, Parallel, Open and Short Circuits”
Electrical-engineering basics
Electrical behaviour becomes easier to reason about when every voltage has a reference and every current has a complete return path.
- Voltage
- Voltage is potential difference between two points. A voltage statement is incomplete unless both points or its reference are known.
- Current
- Current is charge flow through a path. It does not disappear after a component; in a complete circuit it returns to the source.
- Resistance and impedance
- Resistance opposes steady current. Impedance extends that idea to changing signals and can depend on frequency through capacitance and inductance.
- Power and heat
- Electrical power is the rate of energy transfer. Some becomes useful output and some becomes heat that must stay within component and enclosure limits.
- Rating versus operating point
- A rating is a limit or qualified condition, not a target. The operating point must remain inside all relevant voltage, current, power, temperature and timing limits.
How to use this article: Draw the source, load, reference and return path before calculating. Treat exposed or stored electrical energy as hazardous until isolation is proved.
On this page
Series and parallel describe connectivity, not how components happen to look on a page. Two elements are in series when the same branch current must pass through both and their shared node has no other current path. Elements are in parallel when both of their terminals connect to the same two nodes, so they share the same voltage. Open and short describe very different path conditions: one interrupts a path; the other introduces an unintended or intentional low-impedance path.
Series elements share one branch current
Diagram description
A DC source drives resistors R1, R2 and R3 in a single path. Labels show I1 equals I2 equals I3 and the three voltage drops sum to the supply.
Equivalent resistance of series resistors
R_eq = R₁ + R₂ + … + Rₙ; I = V_s/R_eq
Because the same current passes through every resistor, each drop is V_k = IR_k. Kirchhoff's loop rule gives the signed sum V_s = V₁ + V₂ + … when the source rise and resistor drops use consistent directions.
- R_eq
- equivalent resistance seen by the source, Ω
- R₁…Rₙ
- individual series resistances, Ω
- I
- shared branch current, A
- V_s
- applied source voltage for the idealized network, V
Three 100 Ω resistors in series across an ideal 12 V source have R_eq = 300 Ω and I = 40 mA. Each resistor drops 4 V and dissipates 0.16 W under the assumed constant-resistance condition.
| Property | Series result | Common mistake |
|---|---|---|
| Current | Same branch current through every series element | Calling parts series even though their shared node has another branch |
| Voltage | Individual signed drops add to the applied loop voltage | Assuming equal drops when resistances differ |
| Equivalent resistance | Greater than any individual positive resistance | Using the parallel reciprocal formula |
| One open element | Interrupts current through the complete series branch | Assuming zero current means zero voltage everywhere |
| Power | P_k = I²R_k for each applicable ohmic resistor | Ignoring each resistor's individual wattage and voltage rating |
Parallel elements share the same two-node voltage
Diagram description
A DC source supplies two vertical lamp branches. The diagram labels equal supply and branch voltages and shows total current as the sum of branch currents.
Equivalent resistance of parallel resistors
1/R_eq = 1/R₁ + 1/R₂ + … + 1/Rₙ; I_total = I₁ + I₂ + … + Iₙ
Every resistor is across the same node-pair voltage V. For ohmic branches, I_k = V/R_k. Kirchhoff's junction rule expresses conservation of charge: with consistent directions, current entering a node equals current leaving it.
- R_eq
- equivalent resistance of the parallel group, Ω
- R₁…Rₙ
- individual branch resistances, Ω
- I_total
- current delivered to the group, A
- I₁…Iₙ
- individual branch currents, A
A 120 Ω branch and a 240 Ω branch across 12 V draw 100 mA and 50 mA. Total current is 150 mA and R_eq = 12 V / 0.150 A = 80 Ω, less than either branch resistance.
| Property | Parallel result | Common mistake |
|---|---|---|
| Voltage | Same voltage across every branch sharing the two nodes | Assuming every branch current must also be equal |
| Current | Branch currents add algebraically at the junction | Forgetting a newly added branch increases source current for an ideal fixed-voltage source |
| Equivalent resistance | Less than the smallest positive branch resistance | Adding resistances directly |
| One open branch | Other intact branches can continue to operate | Assuming one open stops the whole parallel network |
| Source and wiring | Must carry the total current and tolerate faults | Sizing them from only one branch current |
Series and parallel are properties of a chosen pair or group
A network can contain both. A resistor may be in series with a parallel group, while two other resistors inside that group are parallel with each other. Some bridge networks cannot be reduced by simple series and parallel substitutions at all; Kirchhoff's junction and loop equations or another network method are then required. Always state which elements are being compared.
Open and short circuits are opposite path conditions
Diagram description
Normal, open and short states use the same DC source, source resistance and lamp. The open has a broken connection; the short has a highlighted conductor across the lamp.
| State | Path condition | Current tendency | Voltage consequence |
|---|---|---|---|
| Normal | Intended source-load-return loop is complete | Set by source and load impedances | Load receives its intended terminal voltage within design tolerance |
| Open | Intended path is interrupted or extremely high impedance | Approximately zero in that branch after transients | Substantial voltage may appear across the open points |
| Short | Unintended or deliberate path has very low impedance relative to the load | Potentially very high, limited by total real fault-loop impedance | Bypassed load may have little voltage while conductors and source experience severe stress |
| High-resistance fault | Damaged connection remains conductive but adds unwanted impedance | May be insufficient for protection to operate | Voltage drops and local heating can rise under load |
A first fault-current model
I_fault ≈ V_source / Z_fault-loop
Z_fault-loop includes source internal impedance, conductors, connections, protection, return path and fault or arc impedance. It can vary with time, temperature and source controls. An ideal zero-ohm source and short would imply unbounded current, which is why that idealization cannot predict a real fault.
- I_fault
- prospective or approximate fault current, A
- V_source
- driving source voltage for the modeled interval, V
- Z_fault-loop
- total effective impedance of the complete fault path, Ω
A simplified 12 V source with 0.20 Ω total loop resistance would initially suggest 60 A. Real current may be altered by battery dynamics, wiring temperature, contact or arc behaviour and protective-device operation, so the calculation is only a screen.
One 12 V source shows how connection changes the result
| Connection | Equivalent resistance | Source current | Each resistor voltage | Total power |
|---|---|---|---|---|
| Series | 120 + 120 = 240 Ω | 12/240 = 0.050 A | 6 V | 12 × 0.050 = 0.60 W |
| Parallel | 120/2 = 60 Ω | 12/60 = 0.200 A | 12 V | 12 × 0.200 = 2.40 W |
| One series connection open | Effectively very high for the branch | Approximately 0 A | The open may support nearly the source voltage | Approximately 0 W in the resistors after transients |
| One parallel branch open | One intact 120 Ω branch remains | 0.100 A | 12 V on intact branch | 1.20 W |
| Load terminals shorted | Dominated by real source and fault-loop impedance | Potentially much greater than load current | Near zero across bypassed load in the simple model | Energy is dissipated in source, path, fault and protection |
The parallel pair uses four times the total power of the series pair from the same ideal 12 V source. That is not because parallel connection creates energy; its lower equivalent resistance lets the source deliver more current. A real source may sag, current-limit, heat or shut down, so its terminal behaviour and ratings must be included before applying the ideal result.
Five quick tests for a circuit claim
| Test | Question |
|---|---|
| Topology | Do the alleged series elements truly share one unbranched current, or do parallel elements truly share both nodes? |
| Units | Do Ω, V, A and W remain consistent throughout the calculation? |
| Bounds | Is series R_eq larger than every positive member and parallel R_eq smaller than the smallest? |
| Conservation | Do currents balance at nodes and signed voltage changes sum to zero around loops? |
| Ratings | Can the source, conductors, loads and protective devices tolerate both normal and credible fault conditions? |
These calculations assume resistance is an appropriate model. For operating-point and heating limits, see Resistance, Nonlinear Loads and Heat. To investigate an unexpected open, high-resistance path or missing load voltage without random probing, use the sequence in Using a Multimeter and a Diagnostic Sequence.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for Series, Parallel, Open and Short Circuits?
Trace nodes before writing equations. An ideal wire joins points into one node, even if it bends around the drawing. Redrawing the same node arrangement does not change the circuit. Mark nodes and branches first; then decide which current is shared, which voltage is shared and whether a series-parallel reduction is valid.
Which assumption can change the conclusion?
Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
What can go wrong if I copy the example directly?
An open can still hold dangerous voltage; a short can release dangerous energy. Never touch an open conductor because branch current appears absent, and never create a short as a test. Stored-energy and generation sources can maintain or restore voltage.
How do I verify the result in the real system?
Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Sources and further reading
- Resistors in Series and Parallel — University Physics Volume 2OpenStax, Rice University · 2026-10-13University physics source reviewed for series and parallel current, voltage, power and equivalent-resistance relationships.
- Kirchhoff's Rules — University Physics Volume 2OpenStax, Rice University · 2026-10-13University physics source reviewed for junction current conservation, loop potential sums, nodes and networks not reducible by simple series-parallel substitution.
- Series Circuits — PhysicsOpenStax, Rice University · 2026-10-13Introductory physics source reviewed for series equivalent resistance and the shared-current relationship.
- Parallel Circuits — PhysicsOpenStax, Rice University · 2026-10-13Introductory physics source reviewed for shared branch voltage, branch-current addition and equivalent-resistance bounds.