How do you calculate total resistance in a series circuit?

In a series circuit, total resistance is the sum of all individual resistances: R_total = R₁ + R₂ + R₃ + ... For example, three 100Ω resistors in series have a total resistance of 300Ω.

How do you calculate total resistance in a parallel circuit?

In a parallel circuit, total resistance is found using the reciprocal formula: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. For two resistors, this simplifies to R_total = (R₁ × R₂) / (R₁ + R₂). The total is always less than the smallest individual resistance.

What happens if one component fails in a series circuit?

If any component in a series circuit fails open (breaks), the entire circuit stops working because there is only one path for current. This is why old Christmas tree lights would all go dark when one bulb burned out.

What happens if one component fails in a parallel circuit?

If one component fails in a parallel circuit, the other branches continue to work because each has its own independent path for current. This is why household wiring uses parallel circuits — turning off one light doesn't affect the others.

Are household circuits wired in series or parallel?

Household circuits are wired in parallel. Each outlet and light fixture is connected across the same 120V (or 230V) supply, so they each receive full voltage and operate independently. If one device is turned off or unplugged, the others continue working.

Series vs Parallel Circuits

Q: What is the difference between series and parallel circuits?

In a series circuit, components are connected end-to-end in a single path, so the same current flows through all of them. In a parallel circuit, components are connected across the same two points, creating multiple paths for current. Voltage is shared in series and equal in parallel; current is equal in series and shared in parallel.

A series circuit connects components end-to-end in a single path. A parallel circuit connects components across the same two points, creating multiple paths. These are the two fundamental ways to connect components in any electrical circuit, and they behave very differently in terms of voltage, current, and resistance.

Series circuits

In a series circuit, all components share a single path. Current flows from the voltage source through each component one after another, then back to the source. If you trace the circuit with your finger, there is only one route from start to finish.

Key properties of series circuits

Property	Series behavior	Formula
Current	Same through all components	I_total = I₁ = I₂ = I₃
Voltage	Divides across components	V_total = V₁ + V₂ + V₃
Resistance	Adds up	R_total = R₁ + R₂ + R₃

Series circuit example

A 12V battery powers three resistors in series: R₁ = 100Ω, R₂ = 200Ω, R₃ = 300Ω.

Total resistance:

R_total = 100 + 200 + 300 = 600Ω

Current through the circuit:

I = V / R = 12 / 600 = 0.02 A = 20 mA

Voltage drop across each resistor:

V₁ = I × R₁ = 0.02 × 100 = 2V V₂ = I × R₂ = 0.02 × 200 = 4V V₃ = I × R₃ = 0.02 × 300 = 6V

The voltage drops add up to the source: 2V + 4V + 6V = 12V. This is Kirchhoff's Voltage Law. For more examples, see our voltage drop guide.

Parallel circuits

In a parallel circuit, components are connected across the same two points (nodes). Each component forms its own branch with its own path for current. The voltage across every branch is the same, but the current through each branch depends on that branch's resistance.

Key properties of parallel circuits

Property	Parallel behavior	Formula
Current	Splits across branches	I_total = I₁ + I₂ + I₃
Voltage	Same across all branches	V_total = V₁ = V₂ = V₃
Resistance	Decreases (reciprocal formula)	1/R_total = 1/R₁ + 1/R₂ + 1/R₃

Parallel circuit example

A 12V battery powers three resistors in parallel: R₁ = 100Ω, R₂ = 200Ω, R₃ = 300Ω.

Total resistance:

1/R_total = 1/100 + 1/200 + 1/300 1/R_total = 0.01 + 0.005 + 0.00333 1/R_total = 0.01833 R_total = 54.5Ω

Total current from the source:

I_total = V / R_total = 12 / 54.5 = 0.22 A = 220 mA

Current through each branch:

I₁ = V / R₁ = 12 / 100 = 120 mA I₂ = V / R₂ = 12 / 200 = 60 mA I₃ = V / R₃ = 12 / 300 = 40 mA

The branch currents add up to the total: 120 + 60 + 40 = 220 mA. This is Kirchhoff's Current Law. Notice that the branch with the lowest resistance carries the most current.

Side-by-side comparison

Feature	Series circuit	Parallel circuit
Current	Same everywhere	Splits across branches
Voltage	Splits across components	Same across all branches
Total resistance	Sum of all resistances (increases)	Less than smallest resistor (decreases)
Component failure	Entire circuit stops	Other branches keep working
Wiring complexity	Simple — one loop	More complex — multiple branches
Adding components	Increases total resistance, reduces current	Decreases total resistance, increases total current

Combination circuits (series-parallel)

Most real circuits are neither purely series nor purely parallel — they combine both configurations. A common example is LEDs wired in series strings, where multiple strings are connected in parallel to a power supply. Each string limits current through series resistance, while parallel strings allow more total LEDs.

To analyze a combination circuit, you simplify it step by step: first combine the series parts into single equivalent resistances, then combine parallel groups, and repeat until you have one total resistance. Our voltage drop guide walks through this process with worked examples.

When to use series vs parallel

Use series when:

You need to divide voltage. A voltage divider is two resistors in series, producing a fraction of the input voltage at the midpoint.
You need current-limiting. A resistor in series with an LED limits the current to a safe level. See our LED wiring guide and LED resistor calculator.
Components need the same current. Chaining LEDs in series ensures each gets identical current, producing uniform brightness.

Use parallel when:

Components need the same voltage. Most ICs and modules have a specific operating voltage and should be wired in parallel across the supply.
Independent operation matters. Household wiring is parallel so that turning off one device doesn't affect others.
You need lower total resistance. Parallel resistors reduce total resistance, useful for creating resistance values not available in standard components.
Redundancy is needed. If one path fails in a parallel circuit, others continue working.

Real-world examples

Example	Configuration	Why
LED + resistor	Series	Resistor limits current to protect the LED
Household outlets	Parallel	Each device gets full voltage, operates independently
Battery pack (higher voltage)	Series	Voltages add: 4 × 1.5V AA = 6V
Battery pack (higher capacity)	Parallel	Capacities add: 2 × 2000mAh = 4000mAh at same voltage
LED strip (internal)	Series-parallel	Groups of 3 LEDs in series, groups wired in parallel
Voltage divider (sensor reading)	Series	Two resistors create a proportional voltage for an ADC input

Common mistakes

Assuming voltage is the same in series. In series, voltage divides — each component gets a fraction of the source voltage proportional to its resistance.
Assuming current splits in series. In series, current is the same through every component. Current only splits in parallel circuits.
Using the wrong resistance formula. Series: add directly. Parallel: use the reciprocal formula. Mixing these up gives wildly wrong results.
Wiring LEDs in parallel without individual resistors. LEDs have slightly different forward voltages. In parallel without separate resistors, one LED hogs most of the current and burns out. Always use one resistor per LED, or wire LEDs in series with a shared resistor.

Summary

Series circuits connect components in a single path — current is the same, voltage divides, and resistances add. Parallel circuits create multiple paths — voltage is the same, current divides, and total resistance decreases. Most real circuits combine both. Series is used for current limiting and voltage division; parallel is used when components need the same voltage and independent operation. Understanding these two configurations is the foundation for analyzing and designing any circuit.

Series vs Parallel Circuits: Differences, Examples, and When to Use Each