Calculate equivalent resistance for resistors in series or parallel configurations.
Rtotal = R₁ + R₂ + R₃ + ...
In series, resistors are connected end-to-end. The total resistance is simply the sum of all individual resistances. Current is the same through each resistor.
1/Rtotal = 1/R₁ + 1/R₂ + ...
In parallel, resistors share the same two nodes. The total resistance is always less than the smallest individual resistance. Voltage is the same across each resistor.
Need 15kΩ but only have 10kΩ and 22kΩ? Put them in series for 32kΩ, or parallel for ~6.9kΩ. Combine standard E24 values to create any needed resistance.
Need to dissipate 2W but only have 1/4W resistors? Use multiple resistors in series or parallel to share the power load safely.
Add a small resistor in series with a larger one for fine adjustment. For example, 990Ω + 10Ω = 1000Ω exactly.
Low-value shunt resistors in parallel can achieve very small resistances for high-current sensing applications.
Multiple LEDs with series resistors in parallel branches allow independent current control for each LED while sharing a common power source.
Resistor networks in voltage dividers require understanding both series and parallel combinations for accurate voltage output.
Resistor tolerances combine. In series, the total tolerance percentage stays similar. In parallel, the result is more accurate than individual components.
In series, power is distributed proportionally to resistance. In parallel, power is distributed inversely to resistance. Always verify each resistor stays within its rating.
For exactly two parallel resistors, use the product-over-sum formula: R = (R₁ × R₂) / (R₁ + R₂). This is often faster for quick calculations.
n equal resistors in parallel: R/n. n equal resistors in series: n×R. This is useful for power sharing and creating precise values.