How Ohm's Law Works: I = V / R

Quick Answer

Ohm's law says the current through a resistor is the voltage across it divided by its resistance: I = V / R. Voltage is the electrical push, resistance is the opposition to flow, and current is the resulting stream of charge. For example, 9 volts across 30 ohms gives a current of 9 / 30 = 0.3 amps. Raising the voltage raises the current, while raising the resistance lowers it. Open this circuit simulator, drag a slider, and watch the current and power update as the charge carriers speed up or slow down.

How Ohm's Law Works

The canvas draws a single loop with a battery on the left and a resistor on top. Charge carriers circulate round the loop, and their speed tracks the current. For example, that is why I = V / R: the battery voltage sets how hard the charge is pushed, the resistance sets how much it is held back, and the current is what results. Raise the voltage and the carriers speed up; raise the resistance and they slow to a crawl.

Voltage, Current, and Resistance

The voltage current resistance relationship is the heart of the circuit, and Ohm's law ties the three together as I = V / R, which rearranges to V = I R. Unlike voltage, which is the push from the battery, current is the flow that results, and resistance is what holds it back. To calculate the current from voltage and resistance, divide the voltage by the resistance; used this way the simulator doubles as an ohms law calculator that also shows the charge moving.

• Voltage (V), in volts: the push from the battery that drives charge round the loop. More voltage means more current.
• Resistance (R), in ohms: how strongly the resistor opposes the flow. More resistance means less current.
• Current (I), in amps: the flow of charge, equal to V / R. It is the same at every point in a single loop.

Power and Heat

The resistor turns electrical energy into heat at a rate P = V times I, which is also P = V squared / R. To find the power from voltage and current, multiply the two together. For example, that is why power climbs so steeply as resistance falls: halving the resistance at a fixed voltage doubles the current and doubles the power. In the simulator the resistor glows brighter as the power rises, which is how you can see that a near short circuit dissipates dangerous amounts of heat.

Worked Examples

For example, to protect an LED you might put 5 V across a 100 ohm resistor, so to calculate the current you divide voltage by resistance to get I = V / R = 0.05 A, a safe value. For example, a flashlight bulb of 6 ohms on a 3 V cell draws 0.5 A and glows at P = V times I = 1.5 W. For example, drop the resistance to 2 ohms at 12 V in the simulator and the current jumps to 6 A while the power reaches 72 W, showing why low resistance is risky.

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