Series Circuits

Before you can understand any radio — transmitter, receiver, power supply, or antenna tuner — you need to understand how current flows through a circuit that has more than one component. The series circuit is where that understanding begins. It is the simplest possible arrangement: components connected one after another in a single chain, so that electricity has only one route to travel. Master this, and you have the foundation for everything that follows in electronics.

This lesson assumes you know what voltage, current, and resistance are, and that you have seen Ohm's Law (V = I × R). If those terms feel unfamiliar, revisit Module 1 before continuing. Here we will apply those ideas to real multi-component circuits for the first time.

A series circuit: one unbroken path, one current, three voltage drops that add up exactly to the battery voltage.

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What Makes a Circuit "Series"?

A circuit is called a series circuit when its components are connected end-to-end so that there is only one path through which current can flow. Look at the diagram above: current leaving the battery's positive terminal has no choice — it must pass through R1, then through R2, then through R3, and then return to the battery's negative terminal. There are no branches, no shortcuts, no alternative routes.

Compare this to how lights are wired in your house. Each room's light has its own independent connection back to the fuse box, so switching one light off does not affect the others. That is a parallel circuit (the next lesson). A series circuit is the opposite: turn off one component and the entire chain stops working, because there is no other way for current to flow.

Recognising series connections

Two components are in series if, and only if, every electron that flows through one must also flow through the other. A simple test: trace the circuit from one terminal of the battery to the other. If you pass through both components without encountering any junction (no point where the wire splits into two paths), those components are in series.

In a schematic diagram, series components appear as a single chain of symbols with wire connecting one component directly to the next, with no branches. The moment a wire splits into two or more paths, you no longer have a pure series circuit — you have a parallel element or a series-parallel combination (covered in a later lesson).

Rule 1 — Current is the Same Everywhere

Why is this true?

Think of a garden hose with three kinks in it. Water enters one end, squeezes through the first kink, then through the second, then through the third, and exits the other end. The flow rate — liters per second — is exactly the same at every point along the hose. It has to be, because water cannot disappear inside the hose, and water cannot appear from nowhere inside the hose either.

Electricity obeys the same logic. The "water" is electric charge (electrons in a wire). The "kinks" are the resistors. Because charge cannot be created or destroyed at any interior point of a conductor, the rate at which charge flows past any cross-section of wire — that rate is the current, measured in amperes — must be the same everywhere along a series circuit. This is not an approximation. It is a direct consequence of a fundamental law of physics: the conservation of electric charge.

What this means for measurements

This rule has a powerful practical implication: if you break a series circuit at any point and insert an ammeter (a current-measuring instrument), you will get the same reading regardless of where you break it. Break it between R1 and R2, or between R2 and R3, or between R3 and the battery — the ammeter always reads the same current. This is how you verify that a circuit really is series: measure current at multiple points. If the readings differ significantly, there is a parallel path you did not account for.

A common beginner mistake

New students sometimes think that current is "used up" as it passes through each resistor — that a resistor uses current the way a light bulb uses fuel. This is incorrect. A resistor converts electrical energy into heat, but it does not consume the charge carriers. Every electron that enters R1 exits R1 and continues on to R2. The amount of charge flowing per second (the current) is unchanged. What changes across a resistor is the voltage — the energy per unit of charge — not the charge flow rate itself.

Rule 2 — Resistances Add Together

Why is this true?

Return to the garden hose analogy. Each kink in the hose adds friction that the water must overcome. Three kinks in a row add up their friction — you need more water pressure to push the same flow rate through three kinks than through one. The total friction is simply the sum of the individual frictions.

Resistance is electrical friction. When current must pass through R1, then R2, then R3, it encounters all three resistances in sequence. The battery must push the current through all three, one after another. The total opposition to current flow that the battery experiences is R1 + R2 + R3.

Important consequences of this rule

Adding more resistors in series always increases total resistance. This might seem obvious, but it is worth stating because the rule for parallel circuits works the opposite way — adding more parallel branches decreases total resistance. Keeping these two behaviors separate in your mind is one of the key skills of circuit analysis.

The total resistance is always greater than the largest individual resistor. If you have a 10 Ω, a 100 Ω, and a 1000 Ω resistor in series, the total is 1110 Ω — larger than any one of them. If you ever calculate a series total and it comes out smaller than one of the individual values, you have made an arithmetic error.

Using the rule to find current

Once you know R_total, you can find the circuit current using Ohm's Law. The battery "sees" the whole series chain as if it were a single resistor of value R_total:

This single current value then applies to every component in the circuit, by Rule 1.

Rule 3 — Voltage Drops Add Up to the Supply

Why is this true?

Voltage is electrical potential energy per unit charge — you can think of it as the "height" that electrons fall through. The battery lifts electrons up to a high potential at its positive terminal. As the electrons travel around the circuit and through each resistor, they lose potential energy, giving it up as heat. By the time they return to the battery's negative terminal, they have given up all the energy the battery gave them. The sum of all the energy drops must equal the energy the battery gave — otherwise energy would either be created from nothing or would disappear without trace, which is impossible.

This is actually a preview of Kirchhoff's Voltage Law, which we will cover more formally in a later lesson. In this module, we state it as the voltage sum rule for series circuits.

Voltage is proportional to resistance

Because the current is the same through every component (Rule 1), and because V = I × R (Ohm's Law), a component with a larger resistance has a larger voltage across it. Double the resistance, double the voltage drop. A component that is 1/10th of the total resistance will have 1/10th of the supply voltage across it. The supply voltage is shared out among the components in exact proportion to their resistance values.

This proportional sharing is the basis of the voltage divider, which we cover in a dedicated lesson later in this module. The voltage divider is one of the most commonly used circuits in all of electronics — but it is just a series circuit with two resistors.

Using this rule to check your work

The voltage sum rule gives you a free verification step whenever you solve a series circuit. After calculating the voltage drop across each component, add them all up. The total must equal the supply voltage. If it does not (and you have not made a rounding error), something is wrong with your analysis. This check takes five seconds and has saved countless engineers from submitting wrong answers or building faulty circuits.

Applying Ohm's Law to Each Component

Here is the procedure for analyzing any series circuit from start to finish:

1. Find R_total. Add all resistor values together.
2. Find the current I. Apply Ohm's Law to the whole circuit: I = V_supply / R_total. This current flows through every component.
3. Find the voltage across each component. Apply Ohm's Law individually to each resistor: V_Rn = I × R_n.
4. Verify. Sum all the voltage drops. Check that they equal V_supply.

This four-step procedure works for any series circuit, whether it has two components or twenty. The only arithmetic involved is addition and multiplication/division — there are no simultaneous equations, no complex algebra. That simplicity is why series circuit analysis is the first thing you learn in DC circuit theory.

Units to watch

Be careful with units throughout your calculations. Resistors in a real circuit are often given in kilohms (kΩ = 1000 Ω) and currents often come out in milliamps (mA = 0.001 A). A common mistake is mixing units mid-calculation. The safest approach for beginners: always convert everything to base units first (Ω, V, A) before starting, then convert the answer back to convenient units (kΩ, mA, etc.) at the end.

Power Dissipation in Series Circuits

Every resistor in a series circuit converts electrical energy into heat. The rate at which it does so is its power dissipation, measured in watts (W). For each resistor, power can be calculated three equivalent ways:

All three formulas give the same answer. The most useful one in series circuit analysis is P = I² × R, because you already know I (it is the same everywhere) and you know each R.

Why power matters for component selection

Every resistor has a power rating — the maximum power it can dissipate without overheating and failing. Common ratings are ¼ W, ½ W, 1 W, and 2 W. If your calculation shows a resistor must dissipate 0.4 W, you must use at minimum a ½ W (0.5 W) resistor. Using a ¼ W resistor would cause it to overheat, change value, and eventually burn out. The safety rule of thumb: choose a resistor rated for at least twice the calculated dissipation.

Total power in a series circuit

The total power drawn from the supply equals the sum of the powers dissipated in each component — which is another consequence of energy conservation. You can also calculate total power directly: P_total = V_supply × I. This value equals P_R1 + P_R2 + P_R3 + ...

Power distribution in a series circuit: the largest resistor dissipates the most power and runs the hottest. Always check that each component's power rating exceeds its calculated dissipation.

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Worked Example: Step by Step

Notice how the voltage drops are proportional to resistance. R3 is 3.3 times larger than R1 (330/100 = 3.3), and its voltage drop is 3.3 times larger (6.09/1.85 ≈ 3.3). The voltages are distributed in exact proportion to the resistance values. This is a useful cross-check: look at the ratios.

More Practice Examples

Example 2: Two resistors, finding current and voltage

Example 3: Working backwards — finding a resistor value

Example 4: LED current-limiting resistor (a real-world series circuit)

What Happens When Things Go Wrong

Understanding how series circuits fail is as important as understanding how they work. When you are troubleshooting a piece of equipment, knowing what different faults look like with a voltmeter saves enormous time.

When a component goes open-circuit

An open-circuit failure means the component's internal connection has broken — it now behaves like a gap in the wire. No current can flow through an open circuit. In a series circuit, an open component immediately stops current in the entire circuit, because there is only one path and that path is now broken.

To find which component has gone open, use a voltmeter in DC voltage mode:

• The component that has gone open will have the full supply voltage across it.
• Every other component will have zero volts across it.

Why? With no current flowing, Ohm's Law (V = I × R) gives zero voltage across every working resistor (I = 0). But the open component is effectively an infinite resistance, and all the supply voltage appears across it. This is the voltage divider rule in action: if one resistance is infinitely large compared to all others, it gets nearly all the voltage.

Open-circuit fault diagnosis: with R2 broken, no current flows and the full 12 V appears across R2. R1 and R3 both read 0 V — immediately identifying the faulty component.

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When a component goes short-circuit

A short-circuit failure means the component's terminals are connected directly together with essentially zero resistance — the component is bypassed. Current still flows (the series path is intact through the short), but with less total resistance so more current flows than designed.

To find which component has gone short:

• The shorted component will have zero (or very near zero) volts across it.
• All remaining components will have higher than normal voltage across them (because they are sharing the full supply voltage that the shorted component used to share in).
• The circuit current will be higher than normal.

Short-circuit fault diagnosis: with R2 shorted, it reads 0 V while R1 and R3 read higher voltages than normal and carry 51% more current than designed — potentially enough to overheat them.

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The fuse: a deliberate open-circuit device

A fuse is always wired in series with the circuit it protects. It is a thin wire designed to melt and go open-circuit when the current exceeds a safe level. When the fuse blows, the series circuit is broken and nothing downstream can be damaged by excess current. The fuse sacrifices itself to protect the more valuable components. When you replace a blown fuse, always find out why it blew before fitting a new one — if the fault that caused excess current is still present, the new fuse will blow immediately too.

Series Circuit Solver

Series Circuits in Ham Radio

LED indicator circuits — the simplest ham radio series circuit

Every ham radio accessory you build will eventually need an LED to indicate power on. This is always a series circuit: supply → current-limiting resistor → LED → ground. The resistor does two jobs: it limits current to the LED's rated value (typically 10–20 mA), and it drops the excess voltage that the LED does not need. Using Ohm's Law on this series circuit (the LED is just a component with a fixed voltage drop, not a resistor): R = (V_supply − V_LED) / I_LED. This formula is used millions of times a day by electronics builders worldwide — it is a direct application of the series voltage rule.

Voltage biasing for transistor amplifiers

Every transistor in a radio amplifier — in the receiver front end, in the IF stages, in the audio output — needs a DC operating point set before it can amplify. The most common way to do this is with a voltage divider: two resistors in series across the supply, with the transistor's base connected to the junction between them. This is a series circuit with two resistors. The base voltage equals the supply voltage multiplied by R2/(R1+R2) — a formula you will derive in the voltage divider lesson. Understanding series circuits is the direct prerequisite for understanding how every amplifier in your radio is biased.

Fuse and protection wiring in stations

A fuse is always a series component. In your station, there is a fuse in the power lead between the supply and each piece of equipment. It is wired in series so that if something draws too much current, the fuse opens the series path and protects everything downstream. When a fuse blows repeatedly, you know there is a genuine excess-current problem somewhere in the series circuit — a shorted cable, a failed component, or an overloaded amplifier. The fuse is not the problem; it is the detector.

Voltage drop in supply wiring

Copper wire is not a perfect conductor. A 3-metre run of 1.5 mm² copper wire has a resistance of about 0.075 Ω (0.025 Ω/metre round-trip). When a 100 W transceiver draws 20 A from a 13.8 V supply through this wiring, the series voltage drop in the wire is V = I × R = 20 × 0.075 = 1.5 V. The transceiver only sees 13.8 − 1.5 = 12.3 V — significantly below spec. This is a real, practical series circuit problem. The cure is thicker wire (lower resistance). The RSGB and ARRL recommend 6 mm² wire for runs longer than a few metres to a 100 W transceiver. Series circuit theory tells you exactly why.

Attenuator pads and pi-networks

Fixed attenuators are used between transmitters and dummy loads, between signal generators and receivers, and between antenna ports and receivers to prevent overload. A simple L-pad attenuator consists of one resistor in series with the signal path and one resistor in shunt (to ground). Analysing how much signal passes through requires treating the series resistor and the shunt resistor as a voltage divider — a series circuit with a two-resistor chain. Understanding series circuits is the foundation for attenuator design.

Component ESR in RF circuits

Every practical capacitor and inductor has some internal series resistance — called ESR (Equivalent Series Resistance) for capacitors and winding resistance for inductors. In high-frequency circuits (the IF strip of a receiver, or an antenna tuning network), this ESR acts as a resistor in series with the reactive component, causing signal loss and heating the component. Choosing capacitors with low ESR (ceramic capacitors for RF, not electrolytic) is a direct application of series circuit thinking: minimize the unwanted series resistance in the signal path.