In series
Z = √(R² + X²)
Z = √(R² + (|XL - XC|)²)
In parallel
Z = R + jX
Definitions
Z = Impedance (Ω)
R = Resistance (Ω)
X = Reactance (Ω)
XL = Inductive reactance (Ω)
XC = Capacitive reactance (Ω)
j = √(-1)
Impedance is the total opposition a circuit offers to the flow of alternating current (AC). It combines resistance (R) and reactance (X), and is measured in ohms (Ω).
“The opposition of a circuit to the passage of an alternating electric current.”
The inherent opposition to electric current due to the material's properties. It dissipates energy in the form of heat.
“The tendency of a body to oppose the passage of an electric current.”
The opposition caused by inductance (L) or capacitance (C) in AC circuits. Unlike resistance, reactance stores and releases energy rather than dissipating it.
“Opposition presented to alternating current by inductance or capacitance.”
Use this calculator to compute impedance (Z) using the formula:
( Z = sqrt{R^2 + X^2} )
Where:
Z: Impedance (in Ω)
R: Resistance (in Ω)
X: Reactance (in Ω)
Ideal for electrical engineers, students, and technicians working with AC circuits — quickly calculate impedance without manual math.
A voltage divider is suitable for providing reference voltages to high-impedance loads (such as ADC inputs, op-amp non-inverting inputs, or sensor biasing), but it is not suitable as a power supply for low-impedance loads (such as motors, LEDs, or microcontrollers).
This is because the output voltage will drop significantly when the load draws current, as the load resistance effectively forms a parallel combination with R2, changing the divider ratio. For powering loads, use a voltage regulator (e.g., LDO or switching regulator) instead.
There are two key considerations:
① Ratio determines voltage — the output voltage depends only on the R1/R2 ratio, so any pair of resistors with the same ratio gives the same Vout;
② Absolute values affect current draw — smaller resistor values draw more current from the source (wasting power), while larger values make the output more susceptible to load interference.
A common engineering practice is to keep the divider current at least 10× the load current to minimize loading effects. For most signal-level applications, R1 and R2 in the range of 1kΩ–100kΩ work well.
Voltage dividers are widely used in:
① Level shifting — scaling down a higher voltage signal to match ADC input ranges (e.g., 12V → 3.3V for a microcontroller);
② Sensor interfacing — reading resistive sensors like thermistors, photoresistors, and strain gauges;
③ Biasing — setting DC operating points for transistors and op-amps;
④ Adjustable voltage — using a potentiometer as R2 to create a variable voltage source;
⑤ Feedback networks — setting gain in op-amp circuits.
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