Topic 2 of 4
Series circuits
Series components carry the same current. Their individual potential differences add to the p.d. across the complete path.
For each resistor, V = IR uses the voltage across that resistor and the current through it. Here Vs means the voltage across the complete external network.
Why the current is the same
In a steady unbranched circuit, charge does not continually pile up at one component. The same amount of charge per second passes each position. A resistor transfers energy; it does not consume part of the current before the next resistor.
Each coulomb undergoes successive energy transfers as it passes the components. The work per coulomb across the whole path is the sum of the work per coulomb in its parts, so the potential differences add.
Add the series resistances
For two resistors carrying the same current, V1 = IR1 and V2 = IR2. Adding gives Vs = I(R1 + R2). The single equivalent resistance must therefore be their sum.
One path has the same current; component voltage drops add
These supplied calculation models use fixed resistances, negligible wire resistance and an ideal source. Current arrows indicate direction, not a current scale.
One path: same current through both resistors
The drops 2.0 V and 4.0 V add to 6.0 V. Current is 1.0 A in the whole unbranched path.
Open the only path
Zero steady current does not mean zero source voltage. The only path is broken.
One current, two voltage drops
2.0 Ω and 4.0 Ω across 6.0 V
Assume fixed resistances, negligible wire resistance and an ideal source whose terminal p.d. stays at 6.0 V.
- Total resistance = 2.0 + 4.0 = 6.0 Ω.
- Shared current = 6.0/6.0 = 1.0 A.
- Across 2.0 Ω: V = 1.0 x 2.0 = 2.0 V.
- Across 4.0 Ω: V = 1.0 x 4.0 = 4.0 V.
The drops add to 6.0 V. One coulomb transfers 2.0 J in the first resistor and 4.0 J in the second. The charge passing them has not decreased.
At fixed supply voltage, a larger total resistance means a smaller current. These example values describe a model; practical components must also have suitable ratings and remain close to the assumed temperature.
What an open switch changes
Opening the only path stops the steady current throughout this simple circuit. Each fixed resistor then has V = IR = 0 across it, but the source does not lose its e.m.f. In the ideal open-switch arrangement, the source voltage appears across the gap.
Zero current does not always mean zero voltage. An open gap can have a p.d. across it even though there is no conducting path through it.