Kirchhoff's Laws & Network Analysis
Kirchhoff's current and voltage laws, and how series/parallel resistor networks combine — the toolkit for analyzing any linear circuit.
Ohm's law describes a single component. Kirchhoff's two laws let you analyze an entire network of them.
Kirchhoff's Current Law (KCL)
The sum of currents entering a node equals the sum of currents leaving it. Charge can't accumulate at a node in steady state, so current is conserved.
I_in1 + I_in2 = I_out1 + I_out2 + ...This is the law you reach for when analyzing current splitting across parallel branches, such as a current-sense shunt in parallel with a load.
Kirchhoff's Voltage Law (KVL)
The sum of voltage drops around any closed loop equals zero. Whatever voltage a source supplies must be fully accounted for by the drops across the components in that loop.
V_source = V_drop1 + V_drop2 + ...KVL is what justifies the LED resistor calculation from the previous sub-lesson: the supply voltage must equal the LED's forward voltage plus the drop across the series resistor.
Series and parallel resistance
| Configuration | Equivalent resistance | Current behavior |
|---|---|---|
| Series | R_total = R1 + R2 + ... + Rn | Same current through all |
| Parallel | 1 / R_total = 1/R1 + 1/R2 + ... + 1/Rn | Same voltage across all |
A useful shortcut for exactly two resistors in parallel: R_total = (R1 × R2) / (R1 + R2).
Why this matters for embedded design
Every analog front end — a current-sense amplifier, a voltage divider feeding an ADC, a pull-up resistor on an I2C bus — is sized using nothing more than Ohm's law and KVL/KCL. Getting comfortable with these relationships is what lets you move from copying reference designs to actually deriving the values you need.
Resistors aren't the only passive component on a board, though. The next sub-lesson, Passive Components, covers capacitors and inductors — the parts whose behavior depends on how fast voltage and current are changing.