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.

Key takeaways

• Ohm’s Law is V = I x R, rearrangeable to I = V/R and R = V/I.
• Lower resistance means higher current for the same voltage, which is why shorts are dangerous.
• Electrical power is P = V x I, measured in watts (1 watt = 1 joule per second).
• Heat in a wire follows P = I^2 x R, so doubling current quadruples the heat produced.
• Brownouts are an Ohm’s Law effect: high current causes voltage drop across internal and wiring resistance.

This lesson was adapted from learnfrc.com.