Ohm's Law and Electrical Power

Ohm's Law: the one equation to memorize

The three quantities from the last lesson are tied together by Ohm's Law:

V = I x R

Voltage equals current times resistance. It's a simple product, so rearrange it for whatever you're solving for:

• V = I x R — voltage from current and resistance
• I = V / R — current from voltage and resistance
• R = V / I — resistance from voltage and current

Quick example: a device with 6 ohms on a 12V supply draws I = 12 / 6 = 2 amps. Halve the resistance to 3 ohms and current doubles to 4 amps. Lower resistance means more current — remember that when we get to short circuits, where resistance approaches zero and current tries to skyrocket.

(Wire and resistors follow this straight-line relationship; a few parts like LEDs don't, but the law is still how you reason about every circuit on the robot.)

Power: where the heat comes from

Power is measured in watts (W), and the core formula is:

P = V x I

Combine it with Ohm's Law and you get two variants worth memorizing:

• P = I^2 x R
• P = V^2 / R

The P = I^2 x R form is the one that bites you. Heat lost in a wire scales with the square of current, so doubling the current through a wire quadruples the heat it dumps. That single fact is why thick wire and correctly sized fuses exist.

Run the numbers on your robot

A drive motor pulling 40 amps at roughly 12 volts draws P = 12 x 40 = 480 watts. Multiply across four to six drive motors and it's clear why an FRC battery has to briefly supply 180+ amps during a hard push or a pin against the wall.

Now apply P = I^2 x R to the wire feeding that motor. Say the wire has 0.02 ohms of resistance:

• At 10A: P = 10^2 x 0.02 = 2 watts of heat — fine.
• At 40A: P = 40^2 x 0.02 = 32 watts in that same wire — now it's hot.

A four-fold jump in current produced a sixteen-fold jump in heat. That's the squared term in action, and it's why undersized wire on a high-current motor doesn't just waste energy — it melts insulation and can start a fire.

Brownouts are an Ohm's Law story

When total current spikes, the voltage dropped across the battery's internal resistance and your wiring climbs with it (V = I x R). Push the roboRIO's input low enough and it brownouts, cutting outputs to protect itself (output disable at 6.3V on the roboRIO 1, 6.75V on the roboRIO 2). The fix comes straight from these equations: lower the current (gentler acceleration, current limits in code) or lower the resistance (fresh battery, fat well-crimped 6 AWG leads, tight connections). Knowing whether you have a current problem or a resistance problem tells you which one to reach for.