A series circuit is a circuit in which components are connected end to end so that there is only one path for current. The same current flows through every element, and the source voltage divides among the elements in proportion to their resistances.
Learning objectives
- Calculate the equivalent resistance of resistors in series.
- Explain why the same current flows through every series element.
- Calculate the voltage across each element and verify the voltage sum.
- Recognise the effect of an open circuit in a series path.
Progressive explanation
Start with the plain-language idea, then move into the engineering detail. Each level stands on its own, so you can stop at the depth you need.
Beginner The core idea
The current is the same everywhere in the loop. What changes is the voltage: each component uses part of the source voltage, larger resistances taking a larger share. Add up the voltage across each component and you get back to the source voltage.
Intermediate How it behaves in a circuit
A useful property is that the total resistance of a series combination is always larger than the largest individual resistance. Real components also have tolerances, so the calculated division is nominal; measured voltages can differ slightly. If one element opens, the current falls to zero and the full source voltage appears across the open point, which is why a voltmeter can locate a break.
Advanced Limits, assumptions, engineering detail
At high frequency, the impedance of each element is complex and the voltage division becomes a phasor relationship. Series resonance occurs when inductive and capacitive reactances cancel, producing a minimum impedance and a large current at the resonant frequency. In machine windings, series and parallel groups of coils are combined to obtain the required voltage and current rating, and the mutual coupling between coils means simple resistance addition does not fully describe the behaviour.
Formulas and variables
Units of measurement
| Quantity | Symbol | Unit |
|---|---|---|
| Resistance | R | ohm (Ω) |
| Current | I | ampere (A) |
| Voltage | V | volt (V) |
| Power | P | watt (W) |
Worked examples
Three series resistors
Problem. A 12 V source feeds 10 Ω, 22 Ω and 68 Ω in series. Find the current and the voltage across each resistor.
Solution. R_eq = 10 + 22 + 68 = 100 Ω. I = 12/100 = 0.120 A. Voltages: V₁ = 0.120 × 10 = 1.20 V, V₂ = 0.120 × 22 = 2.64 V, V₃ = 0.120 × 68 = 8.16 V. Check: 1.20 + 2.64 + 8.16 = 12.00 V.
Series circuit with kilohm resistors
Problem. A 12 V supply is connected across 1.0 kΩ, 2.0 kΩ and 3.0 kΩ in series. Find the current and the voltage across the 3.0 kΩ resistor.
Solution. R_eq = 1.0 + 2.0 + 3.0 = 6.0 kΩ. I = 12/6,000 = 2.0 mA. V = I × R = 2.0 mA × 3.0 kΩ = 6.0 V. The other drops are 2.0 V and 4.0 V, summing to 12 V.
Practical applications
- Voltage division and reference setting
- LED current limiting in a string
- Safety and limit switches wired in series
- Multi-cell battery strings
Automotive applications
Series connections appear in switch and sensor circuits: a brake light switch and a fuse are in series with the lamp, so either one can interrupt the circuit. A break anywhere stops the current, and a voltmeter can find it by measuring across each element while the circuit is supposed to be on. Series strings also appear in battery packs, where cell voltage adds and the weakest cell limits the string.
Industrial applications
Industrial control circuits often place emergency stops, limit switches and safety relays in series so that any one of them can drop the contactor coil. This is a fail-safe arrangement: an open contact removes the command to run. For higher voltages, series-connected devices require voltage grading, because unequal leakage currents or capacitances can put excessive voltage across one device.
Measurement procedure
- Measure the current at any point in the series path; it should be the same everywhere within meter accuracy.
- Measure the voltage across each element and add them; the sum should equal the source voltage in a simple series loop.
- To find an open element, measure voltage across each element with the circuit energised; the element with the full source voltage across it is the likely open one.
- De-energise the circuit before measuring resistance, and isolate elements so parallel paths do not affect the reading.
Common mistakes
- Adding voltage drops as if the voltage were the same across every element.
- Expecting the current to be different in different parts of a series path.
- Forgetting that an open circuit in a series path stops current everywhere.
- Adding resistors in parallel when they are actually connected end to end in series.
Safety considerations
- A series circuit is not safer because it has one path; all elements may be at a high potential relative to earth.
- When a series element opens, the full source voltage can appear across the break, which is a shock hazard.
- Isolate and prove dead before working on a circuit, even when a switch appears to be open.