Build and analyze a voltage divider

What is it?

Derive it from scratch (never memorize the bare formula)

HOW — from first principles using Ohm's law + series rules.

Step 1 — Series resistance. $R_1$ and $R_2$ carry the same current $I$ (no branch between them). Total resistance: $R_{total} = R_1 + R_2$ Why this step? In series there's only one path, so resistances add.

Step 2 — Find the current with Ohm's law. $I = \frac{V_{in}}{R_{total}} = \frac{V_{in}}{R_1+R_2}$ Why this step? The whole $V_{in}$ pushes current through the whole loop.

Step 3 — Voltage across $R_2$ (that's $V_{out}$). Ohm's law on $R_2$ alone: $V_{out} = I\cdot R_2 = \frac{V_{in}}{R_1+R_2}\cdot R_2$ Why this step? The output node sits across $R_2$, so its voltage = current × $R_2$.

Step 4 — Clean up. $\boxed{V_{out} = V_{in}\cdot\frac{R_2}{R_1+R_2}}$ Why this step? Just factoring — the fraction $\frac{R_2}{R_1+R_2}$ is $R_2$'s share of total resistance.

Forecast-then-Verify

Common mistakes (steel-manned)

Active recall

Connections

• Ohm's Law — the divider is Ohm's law applied twice.
• Series and Parallel Resistors — series adds; loading brings in parallel.
• Kirchhoff's Voltage Law — drops sum to source.
• Thevenin Equivalent — a divider's output = Thevenin source $V_{out}$ with $R_{th}=R_1\parallel R_2$.
• Wheatstone Bridge — two dividers compared.
• Op-amp Buffer — fixes the loading problem.

Concept Map

Hinglish (regional understanding)