Ohm's Law

Double Voltage, Double Current

current tracks voltage

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

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=12 V4 ohm=3 AI = \frac{12\ \text{V}}{4\ \text{ohm}} = \hl{3}\ \text{A}
The starting circuitA loop with a battery, a resistor, and the ammeter reading the current.12 VA3 A4 ohm3 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→24 V,R unchangedV \rightarrow 24\ \text{V}, \quad R \text{ unchanged}
The same resistor, a larger batteryThe same loop with the resistor unchanged and a larger battery; the ammeter reading is to be found.24 VA4 ohm

Apply Ohm's law to the new voltage

Divide the new voltage by the unchanged resistance.

I=24 V4 ohmI = \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.

VRI8 V4 ohm2 A12 V4 ohm3 A24 V4 ohm6 A\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}
Same resistor, compared voltagesThe same loop with the resistor held fixed while the table compares different battery voltages.24 VA6 A4 ohm6 A

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=6 A=2×3 AI = \hl{6}\ \text{A} = 2 \times \hl{3}\ \text{A}
Twice the voltage, twice the currentThe loop with the larger battery; the ammeter and arrow read the new, larger current.24 VA6 A4 ohm6 A
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.