Series Circuits

Same Current in Series

one path, one flow

In a series circuit, every charge passes through every component, so the current is the same everywhere in the loop.

Example

In a series circuit, every charge passes through every component, so the current is the same everywhere in the loop. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Series means one path

The two resistors are in series because every bit of charge must pass through Ra and then Rb. There is no branch where charge can split.

series⇒one path\text{series} \Rightarrow \text{one path}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 ohm4 ohm

Every part in one row has the same current

Different single-loop circuits can carry different currents, but inside any one series loop the readings match. Each row is one possible loop; left, top, and right stay equal.

IleftItopIright1 A1 A1 A2 A2 A2 A3 A3 A3 A\begin{array}{c|c|c}I_{\text{left}} & I_{\text{top}} & I_{\text{right}} \\1\ \text{A} & 1\ \text{A} & 1\ \text{A} \\2\ \text{A} & 2\ \text{A} & 2\ \text{A} \\3\ \text{A} & 3\ \text{A} & 3\ \text{A}\end{array}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 A2 ohm4 ohm2 A2 A2 A

The same current passes through each part

Because there is only one path, the current cannot be different in the two resistors. The ammeter reads 2 amperes, and the arrows in the loop also read 2 amperes.

Ibattery=IRa=IRb=2 AI_{\text{battery}} = I_{\text{Ra}} = I_{\text{Rb}} = \hl{2}\ \text{A}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 A2 ohm4 ohm2 A2 A2 A
electricity A series circuit has one path, so one current passes through the battery, ammeter, and both resistors.