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Series vs Parallel Circuits: Current, Voltage and Resistance

Connecting parts in a single line is a series connection; connecting them side by side with their ends joined is a parallel connection. In series, the same current flows through every part and the voltage is divided among them. In parallel, the same voltage appears across every part and the current is divided among them. That is why resistances add in series, while in parallel the equivalent resistance is the reciprocal of the sum of reciprocals, smaller even than the smallest resistor. Capacitors are the exception: their formulas are reversed, adding in parallel and combining as reciprocals in series.

AspectSeries connectionParallel connection
Shared quantityCurrent (the same current flows through every part)Voltage (the same voltage appears across every part)
Divided quantityVoltage, divided in proportion to resistance (voltage divider): 2 kΩ and 1 kΩ on 12 V give 8 V and 4 VCurrent, divided in inverse proportion to resistance (current divider): 3 A into 10 Ω and 20 Ω splits into 2 A and 1 A
Equivalent resistanceR = R1 + R2 + …: 100 Ω, 200 Ω and 300 Ω give 600 Ω1/R = 1/R1 + 1/R2 + …: 100 Ω, 200 Ω and 300 Ω give about 54.5 Ω; for two resistors, product over sum
Equivalent capacitance1/C = 1/C1 + 1/C2 + …, so it gets smaller: 10 µF and 22 µF give about 6.88 µFC = C1 + C2 + …, so it adds: 10 µF and 22 µF give 32 µF
Equivalent inductance (no magnetic coupling)L = L1 + L2 + … (same form as resistors)1/L = 1/L1 + 1/L2 + … (same form as resistors)
Part that dissipates more powerThe larger resistance, because the current is the same (P = I²R)The smaller resistance, because the voltage is the same (P = V²/R); two equal resistors share the power equally, but the ratings still need margin (derating)
When one part opensCurrent stops in the whole circuitCurrent keeps flowing through the other parts
Connecting batteriesVoltages add (two 1.5 V cells give 3 V); the capacity (mAh) stays that of one cellThe voltage stays that of one cell; capacities add, so it lasts longer
Examples in electronicsVoltage dividers, current-limiting resistors for LEDs, thermal resistances stacked from junction to case to heat sinkParalleling power MOSFETs to lower on-resistance, many vias and power straps in parallel to reduce IR drop, decoupling capacitors, household outlets

Figures are typical orders of magnitude and vary by process generation and product.

When to use which

Series connection
To divide a voltage (a voltage divider), to pass the same current through every part (such as driving several LEDs at the same current), or to build a higher voltage from batteries.
Parallel connection
To apply the same voltage to every part and keep the others working if one fails (household wiring), or to lower resistance and increase current capacity or capacitance.

FAQ

Why does connecting resistors in parallel lower the resistance?

Because there are more paths for current, so for the same voltage more total current flows. From Ohm's law, R = V/I, more current means a lower equivalent resistance. Whatever resistor is added in parallel, the result is smaller than the smallest resistor: 6 Ω in parallel with 3 Ω gives 18 ÷ 9 = 2 Ω.

Why are the series and parallel formulas reversed for capacitors?

The capacitance of a parallel-plate capacitor is C = εS/d (S is the plate area and d the plate gap). Connecting capacitors in parallel is like enlarging the plate area, while connecting identical capacitors in series is like widening the gap. In equation form, every capacitor in series holds the same charge Q and the voltages Q/C1 + Q/C2 + … add up, giving 1/C = 1/C1 + 1/C2 + ….

Why does the output of a voltage divider drop when a load is connected?

The load is in parallel with the lower resistor, which lowers the resistance of that part. Dividing 10 V with 10 kΩ and 10 kΩ gives 5 V, but a 10 kΩ load across the lower resistor makes that part 5 kΩ, and the output drops to 10 × 5/15 ≈ 3.33 V. Either make the divider resistors much smaller than the load or buffer the output (with a voltage follower).

What should I watch out for when connecting batteries in parallel?

If batteries with different voltages are connected in parallel, current flows from the higher-voltage battery into the lower one. Connect batteries of the same type with matched states of charge. When combining lithium-ion cells, in series or in parallel, use a protection circuit that monitors the voltage of each cell.

Check your understanding

What is the combined resistance of three resistors, 100 Ω, 200 Ω and 300 Ω, connected in series?

  1. AAbout 55 Ω
  2. B600 Ω
  3. C200 Ω
Show answer and explanation

Answer: B. 600 Ω

The combined resistance of resistors in series is their sum: 100 + 200 + 300 = 600 Ω. The same current flows through all three, and the voltage divides in proportion to resistance. Applying 12 V, for example, gives a current of 12 V/600 Ω = 20 mA and voltages of 2 V, 4 V and 6 V across the resistors. With the same three in parallel, the combined resistance is about 55 Ω, smaller than the smallest resistor (100 Ω).

What is the combined resistance of a 6 Ω and a 3 Ω resistor connected in parallel?

  1. A2 Ω
  2. B9 Ω
  3. C4.5 Ω
Show answer and explanation

Answer: A. 2 Ω

For two resistors in parallel, the combined resistance is R1R2/(R1 + R2) (product over sum): 6 × 3/(6 + 3) = 18/9 = 2 Ω. It is also the reciprocal of 1/6 + 1/3 = 1/2. A parallel combination is smaller than its smallest resistor (3 Ω). Both resistors see the same voltage and the current divides in inverse proportion to resistance, so the 3 Ω resistor carries twice the current of the 6 Ω one.

In a parallel-plate capacitor, if the plate area is doubled and the plate spacing is halved, by what factor does the capacitance change? (The dielectric between the plates is unchanged.)

  1. A1 (unchanged)
  2. B4 times
  3. C2 times
Show answer and explanation

Answer: B. 4 times

A parallel-plate capacitor has C = εS/d (ε: permittivity, S: plate area, d: spacing), proportional to area and inversely proportional to spacing. Doubling the area doubles it, and halving the spacing doubles it again, for 2 × 2 = 4 times in total. Filling the gap with a dielectric of relative permittivity εr multiplies the capacitance by εr. Multilayer ceramic capacitors stack many thin dielectric layers to reach large capacitances.

  1. Resistors R1 = 2 kΩ and R2 = 1 kΩ are connected in series, in that order from the positive terminal, across a 12 V DC supply (the other end of R2 goes to the negative terminal). What is the voltage across R2? (No current is drawn from the output.)
  2. A 10 Ω and a 20 Ω resistor are connected in parallel, and a total current of 3 A flows into the combination. What current flows through the 20 Ω resistor?
  3. In a voltage divider made of two 10 kΩ resistors in series across a 10 V DC supply, a 10 kΩ load resistor is connected in parallel with the lower (ground-side) resistor. Which is closest to the output voltage (across the lower resistor)?

Practice Circuit and electromagnetism basics questions

Key terms explained

On-resistance
The resistance of the current path when a power device is on. The smaller it is, the lower the conduction loss.
Thermal resistance
A measure of how hard it is for heat to flow, in °C/W. Multiplying dissipated power by thermal resistance gives the temperature rise. Junction-to-ambient thermal resistance is written θJA.
IR drop
The drop in supply voltage reaching a circuit because current (I) flows through the resistance (R) of the power wiring. It increases delay and can cause malfunctions.
Interconnect via
A conductor that electrically connects the wiring layers above and below it in a multilevel interconnect. It is made by filling a hole in the insulator with metal.
Derating
Using parts with margin below their ratings for voltage, current, temperature and so on, rather than at the full rating, to improve reliability. Typical guidelines are voltage at no more than 70 to 80% of rating, or junction temperature at no more than 125 °C against a 150 °C maximum.

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