Series vs Parallel Circuits
Series vs Parallel Circuits
Definition: In a series circuit, components are connected end-to-end along a single path; in a parallel circuit, components are connected across shared nodes on multiple paths.
How It Works
- Series: the same current flows through every component, since there’s only one path for charge to travel
- Series: the supply voltage divides across the components, proportional to each one’s resistance
- Series: total resistance is the simple sum of each individual resistance
- Series: if any component fails open (breaks), the entire circuit stops conducting, since the single path is interrupted
- Parallel: the same voltage appears across every branch, since all branches connect the same two nodes
- Parallel: the total current from the source divides among the branches, more current flowing through lower-resistance branches
- Parallel: total resistance is always less than the smallest individual branch resistance, since adding paths gives current more ways to flow
- Parallel: if one branch fails open, the other branches keep working independently, since each has its own complete path
- Many real circuits combine both: series-parallel networks, which must be reduced step by step to analyze
- Power dissipation follows the current and voltage split: in series the highest-resistance component dissipates the most power, in parallel the lowest-resistance branch dissipates the most
- Adding an identical resistor in series always increases total resistance; adding an identical resistor in parallel always decreases it, an easy sanity check when reducing a network
Illustration
Under the Hood
Series resistance:
Rtotal = R1 + R2 + R3 + ...Parallel resistance (two resistors):
Rtotal = (R1 × R2) / (R1 + R2)Parallel resistance (general form, any number of resistors):
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...Voltage divider (series circuit):
V2 = Vsupply × (R2 / (R1 + R2))Current divider (parallel circuit, two branches):
I1 = Itotal × (R2 / (R1 + R2))Worked Problem 1: Series total resistance and current Given: A 9V battery drives three resistors in series: 100Ω, 220Ω, and 330Ω. Step 1: Rtotal = 100 + 220 + 330 = 650Ω Step 2: I = V / R = 9 / 650 ≈ 0.01385 A Answer: The circuit draws about 13.85 mA, the same current through all three resistors.
Worked Problem 2: Parallel total resistance Given: Two resistors, 100Ω and 300Ω, are wired in parallel across a 12V supply. Step 1: Rtotal = (100 × 300) / (100 + 300) = 30,000 / 400 Step 2: Rtotal = 75Ω Answer: The combined resistance is 75Ω, lower than either individual resistor.
Worked Problem 3: Voltage divider Given: A 10V supply feeds a series pair, R1 = 1kΩ and R2 = 3kΩ, and the voltage across R2 is needed. Step 1: V2 = 10 × (3000 / (1000 + 3000)) Step 2: V2 = 10 × 0.75 = 7.5V Answer: R2 drops 7.5V, and R1 drops the remaining 2.5V.
Worked Problem 4: Current divider Given: A 2A total current splits between two parallel branches, R1 = 6Ω and R2 = 3Ω. Step 1: I1 (through R1) = 2 × (R2 / (R1 + R2)) = 2 × (3 / 9) Step 2: I1 = 0.667 A, so I2 = 2 - 0.667 = 1.333 A Answer: More current (1.333A) flows through the lower-resistance branch R2, as expected.
Worked Problem 5: Three resistors in parallel Given: 60Ω, 120Ω, and 240Ω resistors are wired in parallel. Step 1: 1/Rtotal = 1/60 + 1/120 + 1/240 = 0.01667 + 0.00833 + 0.00417 Step 2: 1/Rtotal = 0.02917, so Rtotal = 1 / 0.02917 Answer: Rtotal ≈ 34.3Ω, lower than the smallest individual resistor (60Ω), as parallel combinations always are.
Why It Matters
- The wiring choice determines what happens if one component fails: a broken series link stops the whole circuit, while parallel branches keep working independently
- Household and building wiring uses parallel circuits so each outlet or light operates independently and at full mains voltage
- Series wiring is used deliberately in some designs, like LED strings sharing one current-limiting resistor, or safety interlocks where any break should stop the whole system
- Battery packs use series connections to add voltage and parallel connections to add capacity (current capability), and many packs combine both
- Christmas light and appliance safety standards moved toward parallel or hybrid wiring specifically to prevent one failed component from creating an unpredictable open circuit
- Fuses and circuit breakers are placed in series deliberately, so that an overcurrent fault reliably interrupts the entire protected circuit
Common Pitfalls
- Adding parallel resistances the same way as series resistances, forgetting the reciprocal relationship
- Assuming voltage is the same everywhere in a series circuit, when it’s actually current that stays the same and voltage that divides
- Assuming current is the same everywhere in a parallel circuit, when it’s actually voltage that stays the same and current that divides
- Wiring batteries in parallel with mismatched voltage or state of charge, which can cause large, damaging circulating currents between them
- Forgetting that adding a resistor in parallel always lowers total resistance, a common intuition error since “adding more resistors” sounds like it should add more opposition
- Treating a complex series-parallel network as purely one or the other, instead of reducing it step by step
- Assuming an ammeter and voltmeter are interchangeable in placement, an ammeter must go in series with the current path while a voltmeter must go in parallel across the component being measured
- Forgetting that real wires and connectors add small series resistances of their own, which usually can be ignored but matter in high-current or precision circuits
Comparison
| Property | Series | Parallel |
|---|---|---|
| Current | Same through all components | Divides among branches |
| Voltage | Divides across components | Same across all branches |
| Total resistance | Sum of individual resistances | Less than smallest branch |
| Failure behavior | One open component stops everything | Other branches keep working |
| Total capacitance | Decreases (like parallel resistance) | Increases (adds directly) |
| Common use | LED strings, safety interlocks, voltage dividers | House wiring, battery banks, most practical circuits |
Example
Old-style string lights wired in series all go dark if one bulb burns out, since the single conductive path is broken. Household outlets are wired in parallel, so a dead lamp in one room has no effect on outlets elsewhere.
History
- Early electrical distribution, including some of Edison’s original DC systems, used series wiring for street lighting, since it allowed a single generator to drive many lamps efficiently over long distances.
- Series street lighting fell out of favor because a single failed lamp or cut wire could darken an entire street, and later systems adopted safer, more fault-tolerant parallel and constant-current designs.
- The clear mathematical treatment of series and parallel networks solidified alongside Ohm’s and Kirchhoff’s work in the 19th century, forming the foundation of modern circuit analysis.
FAQ
Why does household wiring use parallel circuits instead of series? Parallel wiring keeps full voltage available at every outlet and lets any single device be unplugged, turned off, or fail without affecting the rest of the circuit, which is both safer and more convenient.
Can a circuit be both series and parallel at once? Yes, most real circuits are series-parallel combinations. They’re analyzed by simplifying sub-groups of purely series or purely parallel components into a single equivalent resistance, step by step, until the whole network reduces to one value.
Why is total resistance always lower in parallel than any single branch? Adding a parallel path gives current an additional route, so for the same applied voltage more total current can flow, which by Ohm’s Law means lower effective resistance.
Do capacitors and inductors follow the same series/parallel rules as resistors? Capacitors are the opposite of resistors: they add directly in parallel and combine reciprocally in series. Inductors (ignoring mutual coupling) follow the same rules as resistors: they add directly in series and combine reciprocally in parallel.
Why do old-style Christmas lights all go dark when one bulb burns out, but modern LED strings often don’t? Classic incandescent strings wire every bulb in series on a single loop, so a broken filament opens the whole circuit. Many modern LED strings use parallel sub-groups or shunt devices inside each bulb that bypass a failed unit, keeping the rest of the string lit.
How do engineers simplify a circuit that’s neither purely series nor purely parallel? They identify the smallest self-contained series or parallel sub-groups first, collapse each into a single equivalent resistance, then repeat the process on the simplified network until only one overall value remains.
Related Terms
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