Series and parallel resistor combinations
In a series circuit, resistors are connected end-to-end so total resistance is the sum of all individual values: R_eq = R1 + R2 + R3 + ... Current is identical through every series resistor.
In a parallel circuit, resistors are connected across the same two nodes. The reciprocal of equivalent resistance equals the sum of reciprocals: 1 / R_eq = 1/R1 + 1/R2 + 1/R3 + ... The equivalent resistance is always lower than the smallest individual resistor in the parallel network.
For two resistors in parallel, the formula simplifies to product-over-sum: R_eq = (R1 × R2) / (R1 + R2).
LED series current-limiting resistor sizing
Light Emitting Diodes (LEDs) require a series current-limiting resistor to prevent thermal runaway and destruction from excessive forward current.
Formula: R = (Vs − Vf) / If, where Vs is power supply voltage, Vf is the LED forward voltage drop (typically 2.0V for Red, 3.2V for Blue/White), and If is desired operating current (typically 15 to 20 mA for standard indicator LEDs).
Power dissipated by the resistor is P = (Vs − Vf) × If. Always choose a standard E12/E24 resistor with a power rating at least double the calculated dissipation (e.g. 1/4W or 1/2W).
Inputs for the resistor calculator
Mode
Select parallel network, series network, or LED dropper resistor calculation.
CALCULATOR QUESTIONS
Series, parallel & LED resistor calculator questions
Why do two equal resistors in parallel halve the resistance?
Because adding an identical parallel path doubles the available conductance, allowing twice as much current to flow at the same voltage (e.g. two 100Ω resistors in parallel equal 50Ω).
What happens if you connect an LED without a resistor?
Without a current-limiting resistor, an LED has very low internal resistance once its forward voltage is reached, drawing catastrophic current that burns out the semiconductor junction within milliseconds.