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Impedance of a Resistor
A resistor's impedance in AC analysis is purely real and equal to its resistance.
Interpretation
Impedance of a resistor is purely real and equal to R; it does not depend on frequency.
This means a resistor behaves identically at DC and all AC frequencies (ideally).
Example: R=100Ω → Z_R = 100Ω (with zero phase angle).
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| ZR | Impedance of a resistor | Ω |
| R | Resistance | Ω |
What it means
In AC circuit analysis, the impedance of a resistor is simply its resistance Z_R = R, with no imaginary part. It is real and independent of frequency. This means that a resistor behaves exactly the same at DC and at all AC frequencies (ideally). The voltage and current are in phase (phase angle 0°). The magnitude of impedance is |Z_R| = R, and the power factor is unity. In phasor notation, the voltage across a resistor is in phase with the current. This simplicity makes resistors essential in AC circuits for limiting current and setting bias points. Example: A resistor of 100Ω has an impedance Z_R = 100∠0° Ω. At 50Hz or 1MHz, its impedance remains 100Ω, and there is no phase shift between voltage and current.
Worked example
Impedance of a Resistor – Practical Example
Real‑World| Parameter | Value |
|---|---|
| R | 100 Ω |
| Formula | ZR = R |
Common mistakes
- Resistor impedance: Purely real – no phase shift between voltage and current.
- Frequency independent: Ideal resistors have the same impedance at all frequencies.
- Parasitic effects: Real resistors have inductance and capacitance at high frequencies – not captured.
- Units: Ohms.
Applications
The impedance of a resistor is purely real and equal to R, independent of frequency. This means a resistor behaves identically at DC and all AC frequencies (ideally). Engineers use this to design resistive networks, to set bias points, and to create feedback networks. In AC analysis, the resistor's impedance is represented as a real number, simplifying phasor calculations. By understanding the frequency‑independent nature of resistance, professionals can design stable and predictable circuits. This formula is fundamental to both DC and AC circuit analysis and is essential for all electrical engineers.
- Bias networks for amplifiers and active filters
- Feedback and compensation networks
- Power dissipation and thermal management
- Voltage and current sensing circuits
- Educational foundation of impedance concept
Frequently Asked Questions
The impedance of a resistor is Z_R = R, purely real and independent of frequency.
Zero degrees; current and voltage are in phase.
No, for an ideal resistor, Z_R is constant. In practice, parasitic inductance and capacitance may affect high frequencies.
Z_R = R (0 angle).
Unity (1), because all power is real power.
Series: R_total = R₁ + R₂; Parallel: 1/R_total = 1/R₁ + 1/R₂, same as DC.
I = V/Z_R = V/R, following Ohm's law.
V = I R, in phase with current.
AC circuit analysis, filter design, and power calculations.
Common errors include: 1) using the formula for capacitors/inductors, 2) forgetting the phase, 3) applying to non-ideal resistors, 4) using peak instead of RMS, and 5) combining with other impedances incorrectly.