Voltage Drops Add - Electricity and Electronic Circuits Step by Step

A source gives each coulomb an energy budget. Series resistors spend that budget in drops that add back to the source voltage.

electricity With 12 V across 2 ohm and 4 ohm in series, the drops are 4 V and 8 V, and those drops add back to the source.

Example

A source gives each coulomb an energy budget. Series resistors spend that budget in drops that add back to the source voltage. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The battery gives an energy budget

The battery gives each coulomb 12 joules of energy. In a series loop, the resistors spend that budget one after the other.

V_{\text{source}} = 12\ \text{V}

Each resistor spends part of the budget

The current is the same through both resistors, so each voltage drop is current times resistance.

V_{\text{drop}} = I R

At the same current, bigger resistance drops more voltage

Hold the current at 2 amperes and compare resistor values. The drop grows with resistance because each coulomb spends more energy in the larger resistor.

\begin{array}{c|c|c}I & R & V_{\text{drop}} \\2\ \text{A} & 1\ \text{ohm} & 2\ \text{V} \\2\ \text{A} & 2\ \text{ohm} & 4\ \text{V} \\2\ \text{A} & 4\ \text{ohm} & 8\ \text{V}\end{array}

Compute the two drops

Ra drops 4 volts, and Rb drops 8 volts. The table values are the same values drawn on the two voltage markers.

\begin{array}{c|c|c|c}\text{part} & I & R & V \\\text{Ra} & 2\ \text{A} & 2\ \text{ohm} & 4\ \text{V} \\\text{Rb} & 2\ \text{A} & 4\ \text{ohm} & 8\ \text{V}\end{array}

The drops add back to the source

The two drops are 4 volts plus 8 volts, which uses the full 12 volt battery budget. The diagram and the table are making the same claim.

V_{\text{Ra}} + V_{\text{Rb}} = 4\ \text{V} + 8\ \text{V} = \hl{12}\ \text{V}