Ohm's law

YOU WILL BE ABLE TO

State Ohm's law and use it in all three arrangements (v, i, R).
Define resistance and conductance and their units.
Compute power dissipation in a resistor three ways.
Interpret short and open circuits as limiting cases of resistance.

CA-1 gave you the actors — charge, current, voltage, power. CA-2 introduces the first real component: the resistor, an element that opposes current in strict proportion to the voltage across it. That proportionality is Ohm's law, and it is the single most-used relationship in all of electronics.

v = iR

Ohm's law

The simplest circuit: a source drives a current i = v_s/R through a resistor.

Resistance R is measured in ohms (Ω): one ohm lets one ampere flow when one volt is applied. The law rearranges freely — i = v/R and R = v/i — and you should be able to reach for whichever form the problem hands you without ceremony. Ohm's law assumes the passive sign convention: the current arrow enters the resistor's + terminal. With anti-PSC labels, v = −iR.

Sometimes it's more natural to ask how easily current flows rather than how hard it is. Conductance is the reciprocal of resistance, measured in siemens (S). It will earn its keep in CA-3, where nodal analysis is cleaner in conductances.

G = \frac{1}{R} = \frac{i}{v}

conductance, siemens

A resistor always absorbs power — it converts electrical energy to heat, never the reverse. Substituting Ohm's law into p = vi gives three equivalent forms; use whichever pair of quantities you know.

p = vi = i^2 R = \frac{v^2}{R}

resistor power

WORKED EXAMPLE

The CA-1 capstone, formalized

In the CA-1 capstone you needed 1.3 V across a resistor carrying 10 mA.
R = v/i = 1.3 V / 0.010 A = 130 Ω.
Nearest standard value above: 150 Ω, giving i = 1.3/150 ≈ 8.7 mA — a little dimmer, and safe.

R = 130 Ω exact; 150 Ω standard

WORKED EXAMPLE

Checking a power rating

A 100 Ω resistor has 5 V across it.
p = v²/R = 25/100 = 0.25 W.
A standard ¼ W (0.25 W) resistor would run exactly at its rating — too hot for comfort. Specify a ½ W part, or redesign for less dissipation.

0.25 W — at the limit of a ¼ W part; use ½ W

PRACTICE

A 220 Ω resistor is connected across the Pico's 3.3 V rail. What current flows?

A resistor carries 20 mA with 5 V across it. Find its resistance and its power dissipation, and state whether a ⅛ W (0.125 W) part is adequate.

What is the conductance of a 4 kΩ resistor?

You want to limit an LED (forward drop 2.0 V) to 4 mA from the 3.3 V rail. Compute the exact resistor, pick the nearest standard value above it (E12: 330 Ω is available), and find the actual current.