Series Circuits

Series is the simpler of the two arrangements and the one where the rules are most easily stated. Learn what is constant and what divides, and the arithmetic follows.

The defining property

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A series circuit has exactly one path for current. Everything is connected end to end, so all the current that leaves the source passes through every component in turn.

The current is the same everywhere. This is the thing most worth being sure of, because the intuition that current is consumed by each component is very common and is wrong. A lamp does not use up current; it converts energy while the same current passes through.

Total resistance is always greater than the largest single resistor, which is the check that catches an arithmetic slip.

Working a series circuit

Always in the same order.

1. Add the resistances to get the total.
2. Use Ohm's law on the whole circuit to get the current.
3. That current is the current through every component.
4. Use Ohm's law on each component to get its voltage drop.
5. Check that the drops add to the supply voltage.

Three resistors of 2, 3 and 5 ohms are in series across a 20-volt supply.

• Total resistance: 2 plus 3 plus 5 is 10 ohms.
• Current: 20 divided by 10 is 2 amperes, everywhere.
• Drop across the 2-ohm: 2 times 2 is 4 volts.
• Drop across the 3-ohm: 2 times 3 is 6 volts.
• Drop across the 5-ohm: 2 times 5 is 10 volts.
• Check: 4 plus 6 plus 10 is 20. Correct.

Step 5 is not optional. It catches almost every error in the topic for the cost of one addition.

Voltage divides in proportion

The largest resistance takes the largest share of the voltage.

In the example above the 5-ohm resistor is half the total resistance and takes half the voltage. That is not a coincidence: since the same current flows through all of them, each one's voltage is proportional to its resistance.

That gives a shortcut worth knowing: a component's share of the voltage is its resistance over the total resistance.

What fraction of a 24-volt supply appears across a 6-ohm resistor in series with an 18-ohm resistor?

6 over 24 total is one quarter, so 6 volts.

No need to find the current at all.

Two identical lamps in series across the voltage one lamp is rated for both glow dimly. Each gets half the voltage, and because power goes with the square of voltage, each gives about a quarter of its rated output. A question describing two 60-watt, 120-volt lamps in series across 120 volts wants "both glow dimly".

Batteries in series

Voltages add. Four 1.5-volt cells in series give 6 volts.

They must face the same way. Reversing one subtracts its voltage instead of adding it, which is why a flashlight with one cell in backward is dim or dead rather than merely weaker.

The capacity does not increase. Series cells give more voltage for the same run time; putting cells in parallel is what extends run time at the same voltage.

One failure stops everything

With one path, an open anywhere is an open everywhere.

That is the practical signature of a series circuit and the source of its best question: old holiday light strings were wired in series, so a single failed bulb darkened the whole string. Modern ones are not, which is why one dead bulb now leaves the rest lit.

A switch in series controls everything after it, which is exactly what you want from a master switch.

What you can skip

Across all 1,358 Electronics Information questions in our bank:

• Network theorems - Kirchhoff's laws by name, Thevenin, Norton, superposition - never appear. The series rules in this lesson are what the questions use.
• Wheatstone bridges never appear.
• Long chains of resistors. Series questions use two to four resistors with friendly values. There is no need to practice with awkward decimals.

Where people lose points

Thinking current decreases along the circuit. It does not.

Adding voltages across components instead of recognizing they come from one supply. The drops add to the supply, they do not add on top of it.

Using the supply voltage with one resistor's value to find that resistor's current. Use the total with the total.

Getting a total resistance smaller than one of the resistors. Impossible in series.

Assuming reversing a cell just removes it. It subtracts.

Work one in under a minute

A 4-ohm and a 6-ohm resistor are in series. The voltage across the 4-ohm resistor is 8 volts. What is the supply voltage?

The 8 volts across the 4-ohm resistor gives the current: 8 divided by 4 is 2 amperes, and that current flows through both.

Across the 6-ohm: 2 times 6 is 12 volts.

Supply: 8 plus 12 is 20 volts.

The current is the bridge. Given any one component's voltage and resistance, you have the current, and everything else follows from the current in a series circuit.

Where this leads

Parallel is the other arrangement, and nearly every rule in it is the mirror of a rule here.