Ada Audits the Ohm’s Law Numbers

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

Ada Audits the Ohm's Law Numbers

The chapter applies Ohm’s law across three cases: a 3.3 V GPIO driving a red LED needs a 260-ohm resistor for 5 mA, a 5 V-to-3.3 V divider needs a 0.66 ratio, and a 12 V lamp on a 3-ohm path pulls 4 A and 48 W. The same equation supports an indicator, a sensitive divider, and a high-current load. This audit checks the Ohm’s law numbers to show how the physical consequence changes from brightness to noise to heat.

Companion to the chapter Ohm's Law and Power — every number here comes from that chapter.

Ohm's Law is the bridge from a voltage on the bench to physical current, heat, source capacity, and safe component choice.

1. The LED resistor starts with the voltage that is actually across the resistor. The chapter's GPIO example uses a 3.3 V output and a red LED forward drop of about 2.0 V:

Vresistor = 3.3 V − 2.0 V = 1.3 V

For the 5 mA target current already used in the worked review, convert milliamps to amps before dividing:

R = V / I = 1.3 V / 0.005 A = 260 ohms

The matching heat check can be shown two equivalent ways:

P = V × I = 1.3 V × 0.005 A = 0.0065 W = 6.5 mW
P = I2 × R = 0.0052 × 260 = 0.0065 W

2. The divider example has a ratio requirement before it has a part value. Scaling a 5 V sensor output to a 3.3 V ADC means the output must be 3.3 / 5 = 0.66 of the input. In the divider equation, that is:

Vout / Vin = R2 / (R1 + R2) = 3.3 / 5 = 0.66

The top resistor therefore drops the remaining 5 V − 3.3 V = 1.7 V, so the ideal ratio is R2 / R1 = 3.3 / 1.7 = 1.94. The actual values still need loading, ADC input, noise, and current checks.

3. A simple load turns current into a power and protection decision. The lamp example uses a 12 V source and a 3 ohm path:

Review question Arithmetic shown Audit result
Current demanded by the lamp path I = V / R = 12 V / 3 ohms 4 A
Power converted in the load P = V × I = 12 V × 4 A 48 W
Why this changes the design review 48 W is energy converted every second Check source, switch, wire, fuse, connector, and heat margin before powering.

What the audit buys you: the same equation supports a harmless LED indicator, a sensitive ADC divider, and a high-current load, but the physical consequence changes from brightness to noise to heat.

Every number above is taken from the chapter’s own material and re-derived step by step.