Series Circuits

Series Equivalent Resistance

one bigger opposition

Series resistances add because the same charge must push through each resistor in the single path.

Example

Series resistances add because the same charge must push through each resistor in the single path. 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 resistances add

In a single path, charge must push through both resistors. The total opposition is the sum of their resistances: 2 ohm plus 4 ohm.

Req=RRa+RRbR_{\text{eq}} = R_{\text{Ra}} + R_{\text{Rb}}

Every added resistor raises the series total

Scan three series pairs. In each row the equivalent resistance is just the two resistances added because the same charge must go through both parts.

RaRbReq1 ohm2 ohm3 ohm2 ohm4 ohm6 ohm3 ohm6 ohm9 ohm\begin{array}{c|c|c}R_{\text{a}} & R_{\text{b}} & R_{\text{eq}} \\1\ \text{ohm} & 2\ \text{ohm} & 3\ \text{ohm} \\2\ \text{ohm} & 4\ \text{ohm} & 6\ \text{ohm} \\3\ \text{ohm} & 6\ \text{ohm} & 9\ \text{ohm}\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 ohm4 ohm

Compute the equivalent resistance

Adding gives an equivalent resistance of 6 ohm.

Req=2 ohm+4 ohm=6 ohmR_{\text{eq}} = 2\ \text{ohm} + 4\ \text{ohm} = \hl{6}\ \text{ohm}

The equivalent resistor predicts the same current

A 6 ohm equivalent on the same battery gives 2 amperes, matching the series loop.

I=12 V6 ohm=2 AI = \frac{12\ \text{V}}{6\ \text{ohm}} = \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 Two series resistors can be replaced by one equivalent resistance found by adding their resistances.