A series circuit has just three rules, and all three come straight from physics you already trust: charge is conserved, so the current is the same everywhere; energy is conserved, so the voltages add up; and resistances in line simply add. With those, you can find the current, voltage and resistance anywhere in any series loop.
Three resistors are joined in a single series loop with one battery.
Before reading: is the current through the first resistor larger than, smaller than, or equal to the current through the last one? Write your prediction and a one-sentence reason.
Why one current flows through the whole loop
In a single loop there is nowhere for charge to go but onward, so exactly as much charge enters each component every second as leaves it, the current is the same at every point.
A series circuit is one unbroken path. Because charge is conserved, it cannot accumulate at any point or vanish, so the rate at which charge passes any cross-section, the current, must be identical everywhere in the loop. Whatever current the battery pushes out is the same current flowing through the first resistor, the last resistor and back into the battery.
$$I = I_1 = I_2 = I_3 = \dots \quad\text{(same at every point)}$$
This is why an ammeter reads the same value wherever you place it in a series loop.
In a series circuit the current is the same at every point, $I = I_1 = I_2 = \dots$, because charge is conserved and there is only one path, charge cannot build up or disappear.
Pause, copy the highlighted statement into your book before moving on.
Did you get this? True or false: in a series circuit the current is smaller after passing through a resistor.
Where Vₜ = ΣV and Rₜ = ΣR come from
We just saw that one current flows through everything. That raises a question: how is the supply voltage and resistance shared? This card answers it → energy conservation makes the voltages add, and that forces the resistances to add too.
Each joule of energy the battery gives to a charge is spent crossing the components in turn, so the energy spent per charge (voltage) must add up to the energy supplied per charge.
As a charge travels around the loop, it gives up energy at each component. By conservation of energy, the total energy given up per charge equals the energy supplied per charge, so the supply voltage equals the sum of the voltage drops:
$$V_T = V_1 + V_2 + V_3 + \dots$$
Since the same current $I$ flows through each component, $V_1 = IR_1$, $V_2 = IR_2$, and so on. Substituting into $V_T = IR_T$ and dividing by $I$ gives the resistance rule:
$$R_T = R_1 + R_2 + R_3 + \dots$$
A $12\ \text{V}$ battery is connected in series with a $3.0\ \Omega$ and a $5.0\ \Omega$ resistor. Find the total resistance, the current, and the voltage across each resistor.
In series, total resistance $R_T = R_1 + R_2 + \dots$ and total voltage $V_T = V_1 + V_2 + \dots$. Find the current from $I = V_T/R_T$, then each voltage drop from $V_n = IR_n$; the drops sum to the supply voltage.
Add the highlighted rules to your notes before the check below.
Quick check: Two resistors, $4.0\ \Omega$ and $6.0\ \Omega$, are in series with a $20\ \text{V}$ supply. What is the current in the circuit?
Pattern A, Calculate then check
A $9.0\ \text{V}$ battery is in series with three resistors: $1.0\ \Omega$, $2.0\ \Omega$ and $6.0\ \Omega$. In your book: (1) find the total resistance; (2) find the current; (3) find the voltage across each resistor; (4) confirm the three voltage drops add to $9.0\ \text{V}$ and write one sentence saying which conservation law that confirms.
Fill the blanks: Complete the statement about CURRENT in a series circuit.
A series circuit has only one path, so the current has the magnitude at every point in it. Adding a further resistor in series makes that current .
Dot point: Account for the magnitude of current at any point in a series circuit
Why the loop slows everywhere when you add resistance
We just learned that series resistances add. That raises a question: what does this do to the current? This card answers it → a higher total resistance with the same supply voltage means a smaller current, everywhere at once.
Because the whole loop shares one current, anything that raises the total resistance throttles that single current, so adding a resistor anywhere slows the charge everywhere.
For a fixed supply voltage, the current is $I = V_T / R_T$. Adding another resistor in series increases $R_T$, so $I$ falls. Since the same current flows through the entire loop, every component carries this reduced current, that is why "adding resistance in one place slows the charge everywhere". It also explains the dimming hook: more series components share the same fixed voltage and run on a smaller current, so each is dimmer.
Because $I = V_T/R_T$ and the loop shares one current, adding a resistor in series raises $R_T$ and lowers the current everywhere in the circuit. More series components means a smaller shared current.
Pause, copy the highlighted reasoning into your book before the check below.
Last check: Decide if the statement is true or false.
Adding another resistor in series with a fixed supply voltage increases the total resistance and therefore decreases the current in the whole circuit.
Two truths, one lie: three of these statements about VOLTAGE in a series circuit are correct. Which one is the lie?
Dot point: account for the total voltage of a series circuit being the sum of the voltages of its components using conservation of energy and V_total = V1 + V2 + …
A fresh set drawn from this lesson's question bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
ApplyBand 5(4 marks) 1. A $24\ \text{V}$ battery is connected in series with a $2.0\ \Omega$ and a $4.0\ \Omega$ resistor. Calculate the total resistance, the current, and the voltage across each resistor, and show that your voltages are consistent with conservation of energy.
1 mark: $R_T = 6.0\ \Omega$ · 1 mark: $I = 4.0\ \text{A}$ · 1 mark: $V_1 = 8.0\ \text{V}$ and $V_2 = 16\ \text{V}$ · 1 mark: $V_1 + V_2 = 24\ \text{V}$ equals the supply, confirming conservation of energy
ExplainBand 5(3 marks) 2. Account for the fact that the current has the same magnitude at every point in a series circuit, and explain why adding a further resistor in series reduces that current.
1 mark: there is only one path, and charge is conserved so it cannot accumulate or disappear · 1 mark: therefore the same rate of charge flow passes every point · 1 mark: adding resistance raises $R_T$, and $I = V/R_T$ with fixed $V$ means a smaller current
Dot point: Account for the magnitude of current at any point in a series circuit
ExplainBand 5(3 marks) 3. Three unequal resistors are connected in series across a $12\ \text{V}$ supply. Without performing any calculation, explain why the three voltages across them must add to $12\ \text{V}$, and state which resistor has the largest voltage across it and why.
1 mark: each coulomb gains $12\ \text{J}$ from the supply and must give all of it up in one trip round the loop · 1 mark: so the energy lost per coulomb in the components sums to the energy gained per coulomb, i.e. the voltages sum to $12\ \text{V}$ · 1 mark: the largest resistance has the largest voltage, because $V = IR$ with the same current through all three
Dot point: account for the total voltage of a series circuit being the sum of the voltages of its components using conservation of energy and V_total = V1 + V2 + …
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set from the lesson bank.
Q1 (4 marks): In series the resistances add: $R_T = R_1 + R_2 = 2.0 + 4.0 = 6.0\ \Omega$. The single series current is $I = V_T / R_T = 24 / 6.0 = 4.0\ \text{A}$, and this same current flows through both resistors. The voltage drops are $V_1 = IR_1 = 4.0 \times 2.0 = 8.0\ \text{V}$ and $V_2 = IR_2 = 4.0 \times 4.0 = 16\ \text{V}$. Adding these gives $V_1 + V_2 = 8.0 + 16 = 24\ \text{V}$, which equals the supply voltage. This confirms conservation of energy: each charge gives up exactly the energy per coulomb supplied by the battery as it crosses the two resistors.
Q2 (3 marks): A series circuit provides only one conducting path, so every charge that passes one point must go on to pass every other point. Charge is conserved and does not accumulate anywhere in the wires or components, so the rate at which charge passes any cross-section must be identical everywhere in the loop. Since current is precisely that rate of charge flow, the current has the same magnitude at every point, regardless of the resistances present. Adding a further resistor in series increases the total resistance, because in series the resistances add. The supply voltage is unchanged, so from $I = V_T/R_T$ a larger denominator gives a smaller current. Every component then carries this reduced current, which is why adding lamps in series makes them all dimmer.
Q3 (3 marks): Voltage is energy per unit charge. Each coulomb of charge is given $12\ \text{J}$ of energy by the supply, and because there is a single path it must travel through all three resistors and return to the supply. It cannot arrive back carrying leftover energy, and it cannot lose more than it was given, so the energy it gives up in the three components must total exactly $12\ \text{J}$ per coulomb. Expressed as energy per coulomb, that is precisely the statement that the three voltages add to $12\ \text{V}$; it is conservation of energy written in circuit language. The largest voltage is across the largest resistance. The current is identical through all three because they are in series, so by $V = IR$ the voltage across each is directly proportional to its resistance, and the biggest resistance therefore takes the biggest share.
You can now use the three series rules, one current, $V_T = \Sigma V$ and $R_T = \Sigma R$, to solve a series loop. Next lesson does the same for parallel circuits, where the current divides between branches.
↩ Back to focus-area hubAt the start you predicted whether the current changes along a series loop. The answer: it is the same at every point, because charge is conserved and there is only one path. What is shared out is the voltage (energy), not the current. If you predicted the current shrinks, revisit Card 1.
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.
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