Double Voltage, Double Current - Electricity and Electronic Circuits Step by Step

With resistance held fixed, current is proportional to voltage. Double the battery and the current doubles too.

electricity Same 4 ohm resistor, battery doubled from 12 V to 24 V: the current doubles from 3 A to 6 A, because at fixed resistance current is proportional to voltage.

Example

With resistance held fixed, current is proportional to voltage. Double the battery and the current doubles too. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Recall the flagship circuit

Start from the Ohm's law flagship: 12 volts across 4 ohm gives a current of 3 amperes.

I = \frac{12\ \text{V}}{4\ \text{ohm}} = \hl{3}\ \text{A}

Now double the battery voltage

Keep the same 4 ohm resistor, but double the battery to 24 volts. The ammeter reading is what we want to find.

V \rightarrow 24\ \text{V}, \quad R \text{ unchanged}

Apply Ohm's law to the new voltage

Divide the new voltage by the unchanged resistance.

I = \frac{24\ \text{V}}{4\ \text{ohm}}

Fixed resistance makes current track voltage

Now compare three voltages while the resistor stays at 4 ohm. Each row uses the same divider, so the current grows in step with the voltage.

\begin{array}{c|c|c}V & R & I \\8\ \text{V} & 4\ \text{ohm} & 2\ \text{A} \\12\ \text{V} & 4\ \text{ohm} & 3\ \text{A} \\24\ \text{V} & 4\ \text{ohm} & 6\ \text{A}\end{array}

The current doubles

The current is now 6 amperes, exactly twice the 3 amperes from before. With resistance held fixed, current is proportional to voltage: double the push, double the flow.

I = \hl{6}\ \text{A} = 2 \times \hl{3}\ \text{A}