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People also ask about ac impedence and dc impedence

People also ask about ac impedence and dc impedence

22-07-2025

Questions about ac impedence and dc impedence

1

What is the difference between ac impedence and dc impedence?

2

What is the relationship between ac impedence and dc impedence?

3

How do you convert dc resistence to ac resistence?

4

Are impedence and resistence the same?

5

How to measure dc resistence with a multimeter?

What is the difference between ac impedence and dc impedence?

The key difference between AC impedance (Z) and DC impedance lies in how they account for resistance and reactance under different types of electrical signals (alternating current vs. direct current). Here's a breakdown:

DC Impedance

Definition: In a DC (Direct Current) circuit, the impedance is simply the resistance (R) of the component (e.g., resistor, wire).
Behavior:

DC signals have a constant voltage/current (no frequency, $f = 0$ ).
Inductors act as short circuits (no inductive reactance, $X_{L} = 0$ ).
Capacitors act as open circuits (no capacitive reactance, $X_{C} = \infty$ ).

Formula:
$Z_{DC} = R (only resistance matters)$
Example:

A resistor’s DC impedance is just its resistance (e.g., 100 Ω).
An inductor in DC behaves like a wire (impedance ≈ 0 Ω).

2. AC Impedance (Z)

Definition: In an AC (Alternating Current) circuit, impedance includes resistance (R) and reactance (X) due to frequency-dependent effects from inductors (L) and capacitors (C).
Behavior:

AC signals vary with time (frequency $f > 0$ ).
Inductors introduce inductive reactance ( $X_{L} = 2 π f L$ ).
Capacitors introduce capacitive reactance ( $X_{C} = \frac{1}{2 π f C}$ ).

Formula:
$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}} (magnitude)$ $Z = R + j (X_{L} - X_{C}) (complex form)$
(where $j$ is the imaginary unit)
Phase Shift: AC impedance also causes a phase difference between voltage and current.
Example:

A 10 mH inductor at 1 kHz has $X_{L} = 62.8 Ω$ .
A 1 µF capacitor at 1 kHz has $X_{C} = 159 Ω$ .

3. Key Differences

Feature	DC Impedance	AC Impedance
Components	Only resistance ( $R$ )	Resistance + Reactance ( $X$ )
Frequency	$f = 0$ (no effect)	$f > 0$ (critical)
Inductor	Short circuit ( $Z \approx 0$ )	$Z = j X_{L} = j 2 π f L$
Capacitor	Open circuit ( $Z \approx \infty$ )	$Z = - j X_{C} = \frac{- j}{2 π f C}$
Phase	No phase shift	Voltage/current phase shift

What is the relationship between ac impedence and dc impedence?

The relationship between AC impedance (Z) and DC impedance is fundamental in understanding how circuits behave under different electrical signals. Here’s a concise breakdown of their connection:

Core Relationship

DC impedance is a subset of AC impedance:

Inductive reactance ( $X_{L} = 2 π f L \to 0$ ).
Capacitive reactance ( $X_{C} = 1 / (2 π f C) \to \infty$ ).
AC impedance ( $Z_{AC}$ ) generalizes to DC impedance ( $Z_{DC}$ ) when frequency ( $f$ ) approaches zero:
$Z_{AC} = R + j (X_{L} - X_{C}) \overset{f = 0}{\to} Z_{DC} = R$

Resistance ( $R$ ) is common:
The resistive component ( $R$ ) is present in both AC and DC regimes, representing energy dissipation.

How do you convert dc resistence to ac resistence?

To convert DC resistance (Rdc) to AC resistance (Rac), we must account for two key phenomena that increase resistance in alternating current (AC) systems:

Skin Effect (ys) – Current tends to flow near the conductor's surface at high frequencies, reducing the effective cross-sectional area.
Proximity Effect (yp) – Nearby conductors carrying AC current induce uneven current distribution, further increasing resistance.

Conversion Formula

The AC resistance is calculated by adding correction factors for skin and proximity effects to the DC resistance:

$R_{a c} = R_{d c} (1 + y_{s} + y_{p})$

where:

$R_{a c}$ = AC resistance (Ω/m or Ω/ft)
$R_{d c}$ = DC resistance (Ω/m or Ω/ft) at maximum operating temperature
$y_{s}$ = Skin effect correction factor
$y_{p}$ = Proximity effect correction factor

Steps to Calculate AC Resistance

Determine DC Resistance (Rdc)

Measure or calculate the conductor’s DC resistance at its maximum operating temperature.
For copper or aluminum conductors, refer to standard resistivity tables.

Calculate Skin Effect Factor (ys)

$μ$ = Permeability of the conductor (H/m)
$ρ$ = Resistivity (Ω·m)

Depends on frequency (f), conductor material, and diameter (D).
For round conductors:
$y_{s} = \frac{1}{2} {(\frac{π f μ}{ρ})}^{0.5} D$
where:

Calculate Proximity Effect Factor (yp)

Depends on conductor spacing, frequency, and material.
For parallel conductors:
$y_{p} = \frac{1}{2} {(\frac{π f μ}{ρ})}^{0.5} {(\frac{D}{s})}^{2}$
where $s$ = center-to-center spacing between conductors.

Compute AC Resistance (Rac)

Apply the correction factors:
$R_{a c} = R_{d c} (1 + y_{s} + y_{p})$

Key Observations

At low frequencies (e.g., 50/60 Hz power lines), skin and proximity effects are small, so $R_{a c} \approx R_{d c}$ $R_{a c} \approx R_{d c}$ .
At high frequencies (e.g., RF, high-power transmission), $R_{a c}$ $R_{a c}$ can be significantly higher than $R_{d c}$ $R_{d c}$ .

Are impedence and resistence the same?

Key Differences

Aspect	Resistance (R)	Impedance (Z)
Signal Type	Only applies to DC.	Applies to AC (or transient signals).
Components	Pure real value (no phase shift).	Complex value: $Z = R + j X$ (real + imaginary).
Frequency Dependence	Independent of frequency.	Depends on frequency (due to reactance $X$ ).
Phase Effects	No phase difference between voltage/current.	Causes phase shift (due to reactance).
Energy Dissipation	Always dissipates power ( $P = I^{2} R$ ).	May store/release energy (if reactance dominates).

Mathematical Relationship

Impedance generalizes resistance by adding reactance ( $X$ ):

$Z = R + j X$

where:

$R$ = Resistance (real part, dissipates energy).
$X$ = Reactance (imaginary part, stores/releases energy):

Inductive reactance ( $X_{L} = ω L$ ) → Opposes AC via magnetic fields.
Capacitive reactance ( $X_{C} = - 1 / ω C$ ) → Opposes AC via electric fields.

Special Cases

Pure DC ( $f = 0$ ) → $X_{L} = 0$ , $X_{C} = \infty$ , so $Z = R$ .
Pure AC with no resistance → $Z = j X$ (e.g., ideal inductor/capacitor).

How to measure dc impedence with a multimeter?

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