This lesson involves circuit analysis that applies directly to live equipment you will troubleshoot. Industrial control panels contain series and parallel combinations of loads. Knowing circuit topology lets you predict what will happen when a device fails — and why.
No hands-on energized work in this lesson. All calculations and diagrams are for conceptual understanding. Apply lockout/tagout (LOTO) procedures before touching any physical panel component.
Short circuits in parallel branches can draw thousands of amperes instantaneously. Overcurrent protection devices are your last line of defense — never bypass fuses or circuit breakers. Verify OCP ratings before modifying any circuit.
Every electrical circuit is either series, parallel, or a combination of the two. Understanding the behavior rules for each topology allows you to predict how voltage, current, and resistance distribute throughout any circuit — before you ever touch a meter.
This lesson builds directly on Ohm’s Law (Lesson 5.5). Once you can classify a circuit’s topology, you can reduce it to a single equivalent resistance and apply V = IR to solve for any unknown quantity.
Series vs. parallel topology determines fault behavior. An open in a series control circuit kills the whole output. An open in a parallel power circuit only kills one branch. Misreading the topology while troubleshooting costs time — and can create dangerous conditions if loads are re-energized unexpectedly. This lesson is the foundation for schematic reading (5.15) and control circuit troubleshooting (5.14).
Upon completing this lesson, you will be able to:
In a series circuit, components are connected end-to-end along a single conduction path. Current has only one route through the circuit — it must flow through every component in order.
Because there is only one path, the same current flows through each component.
IT = I1 = I2 = I3Each component uses a portion of the supply voltage. All drops must sum to the total.
VT = V1 + V2 + V3Total resistance is the sum of all individual resistances. Adding components always increases RT.
RT = R1 + R2 + R3Given: R1 = 10Ω, R2 = 15Ω, R3 = 25Ω, Supply = 100V
R_T = 10 + 15 + 25 = 50ΩI = V / R_T = 100 / 50 = 2A (same through all components)V₁ = 2 × 10 = 20VV₂ = 2 × 15 = 30VV₃ = 2 × 25 = 50V20 + 30 + 50 = 100V ✓ALL current stops immediately — the entire circuit de-energizes. This is the principle behind series safety devices: E-stops, safety relays, door interlocks, and light curtains. One open anywhere = zero output.
The shorted element is bypassed. Voltage re-distributes across remaining elements. If a current-limiting resistor shorts, circuit current increases — potentially damaging remaining components. If a fuse is shorted (never do this intentionally), downstream protection is lost.
In a parallel circuit, components are connected across the same two nodes, providing multiple independent current paths. Each branch sees the full supply voltage.
Every branch connects directly across the supply — all branches see identical voltage.
VT = V1 = V2 = V3Total current from the supply is the sum of all branch currents. More branches = more total current.
IT = I1 + I2 + I3RT is always less than the smallest branch. More parallel paths = easier current flow.
1/RT = 1/R1 + 1/R2 + 1/R3Given: R1 = 6Ω, R2 = 12Ω, R3 = 24Ω, Supply = 24V
I₁ = 24/6 = 4AI₂ = 24/12 = 2AI₃ = 24/24 = 1AI_T = 4 + 2 + 1 = 7AR_T = V/I_T = 24/7 = 3.43Ω1/R_T = 1/6 + 1/12 + 1/24 = 4/24 + 2/24 + 1/24 = 7/24R_T = 24/7 = 3.43Ω ✓Only the opened branch loses power. All other branches continue operating normally. Parallel circuits are more fault-tolerant for power distribution — a single failed component does not collapse the entire system.
A short in one branch presents near-zero resistance across the full supply voltage, drawing massive fault current. This trips the main overcurrent protection device, de-energizing ALL branches. One short takes down the entire parallel circuit.
Real industrial circuits are almost always combinations of series and parallel sections. The approach: simplify from the inside out — reduce parallel groups first, then treat the result as a series resistor, repeating until you have a single equivalent resistance.
R1 = 20Ω ∥ R2 = 20Ω (parallel), in series with R3 = 5Ω. Supply = 50V.
R_p = 20/2 = 10ΩR_T = 10 + 5 = 15ΩI_T = 50/15 = 3.33AV_p = 3.33 × 10 = 33.3VV₃ = 3.33 × 5 = 16.7V33.3 + 16.7 = 50V ✓R1 = 4Ω (series) → R2 = 6Ω ∥ R3 = 12Ω (parallel) → R4 = 8Ω (series). Supply = 120V.
R₂₃ = (6×12)/(6+12) = 72/18 = 4ΩR_T = 4 + 4 + 8 = 16ΩI_T = 120/16 = 7.5AV_R1 = 7.5 × 4 = 30VV_R23 = 7.5 × 4 = 30V (parallel section)V_R4 = 7.5 × 8 = 60V30 + 30 + 60 = 120V ✓I₂ = 30/6 = 5A I₃ = 30/12 = 2.5A5 + 2.5 = 7.5A ✓(1) Identify parallel sections (same two nodes, multiple paths). (2) Reduce each to its equivalent resistance. (3) What remains is a series string. (4) Apply Ohm’s Law. Sketch a simplified redraw at each step to avoid errors.
The series and parallel rules are derived from two fundamental laws established by Gustav Kirchhoff in 1845. This is an awareness-level introduction — full application is a Level 2+ topic.
Energy cannot be created or destroyed in a circuit loop. All voltage supplied by sources must equal the sum of voltage consumed by loads. This proves the series voltage rule: V₁ + V₂ + V₃ = V_T.
Charge cannot accumulate at a node. Whatever current flows in must flow out. This proves the parallel current rule: I_T = I₁ + I₂ + I₃.
At Level 1 (Awareness), recognize KVL and KCL by name and understand that the series/parallel rules derive from them. Applying KVL and KCL to multi-loop circuits with simultaneous equations is a Level 2 competency covered in Lesson 5.12.
Enter resistor values and supply voltage. Switch tabs to toggle between series and parallel modes. Results show full worked solution.
Use this table when troubleshooting. Circuit topology determines how faults propagate — knowing this before you meter anything cuts diagnostic time significantly.
| Fault Type | Location | Series Circuit Effect | Parallel Circuit Effect |
|---|---|---|---|
| Open Circuit | Any one element | All outputs de-energize — circuit fully dead | Only that branch fails — all others remain normal |
| Short Circuit | Any one element | Current increases; remaining resistances heat up; fuse/breaker may trip | Massive fault current → OCP trips → ALL branches de-energize |
| High Resistance | One element | Less current everywhere; all outputs see reduced voltage (dim lights, sluggish motor) | That branch draws less current; other branches unaffected |
| Ground Fault | Conductor/wiring | Location-dependent; may trip GFCI or ground fault relay; downstream loads may see reduced voltage | Location-dependent; may trip GFCI on that branch or entire feeder |
| Intermittent Contact | Connection point | Intermittent loss of all output — arc potential at loose connection | Intermittent loss of that branch only — other branches stable |
| Low Supply Voltage | Source / feeder | All components see reduced voltage proportionally | All branches see reduced voltage; high-current branches draw proportionally less |
All loads fail simultaneously? Look for an open in a series element upstream: fuse, breaker, E-stop, contactor, overload. Only one load fails while others are fine? Look for an open within that branch: branch fuse, connection, or the load itself. These two patterns instantly narrow a fault to series vs. parallel topology.
Read each scenario carefully. Identify the circuit topology before clicking Reveal Answer. The reasoning process is as important as the answer.
These scenarios represent common arrangements found on 480V MCC panels and 120VAC control circuits in industrial facilities.
Select your answer for each question and click "Check Answer" for immediate feedback. Score is displayed after all five are answered.
Industrial electrical systems combine both topologies deliberately: series for safety interlocks (E-stops, door interlocks, safety relays) so any single open de-energizes the hazard; parallel for power distribution (lighting, motors, solenoids) so a single failed load does not kill the system. Identifying which topology you are looking at in a schematic is the first step in every troubleshooting task.
| Parameter | Series | Parallel |
|---|---|---|
| Total Resistance | Rₜ = R₁ + R₂ + R₃ | 1/Rₜ = 1/R₁ + 1/R₂ + ... (product/sum for two) |
| Current | Iₜ = I₁ = I₂ (same) | Iₜ = I₁ + I₂ + I₃ (adds) |
| Voltage | Vₜ = V₁ + V₂ + V₃ (adds) | Vₜ = V₁ = V₂ (same) |
| Open fault effect | All loads de-energize | Only that branch fails |
| Short fault effect | More current; heat; possible fuse trip | OCP trips; all loads de-energize |
5.7 — Single-Phase and Three-Phase Power builds on today’s circuit analysis to explain how industrial three-phase systems distribute power more efficiently than single-phase. You will apply series-parallel concepts to understand how three-phase wye and delta configurations behave under load and fault conditions.