Electrical impedance

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Impedance_symbol_comparison

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Resistors

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File:Impedances in series|thumb|Impedances_in_series]]]] Electrical impedance

Electrical impedance is a measure of the opposition that a circuit presents to a current when a voltage is applied. Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance which has only magnitude. The symbol for impedance is usually Z and it may be represented by complex numbers.

Definition

Impedance is defined as the ratio of the voltage to the current in an AC circuit. It is given by the formula: \[ Z = \frac{V}{I} \] where:

• \( Z \) is the impedance, measured in ohms (Ω)
• \( V \) is the voltage, measured in volts (V)
• \( I \) is the current, measured in amperes (A)

Components of Impedance

Impedance is composed of two components:

• Resistance (R): The real part of impedance, which represents the opposition to the flow of direct current (DC).
• Reactance (X): The imaginary part of impedance, which represents the opposition to the flow of alternating current (AC) due to inductance and capacitance.

The impedance can be expressed in complex form as: \[ Z = R + jX \] where:

• \( R \) is the resistance
• \( X \) is the reactance
• \( j \) is the imaginary unit

Types of Reactance

Reactance can be further divided into:

• Inductive reactance (X_L): Caused by inductors in the circuit, given by \( X_L = 2\pi f L \)
• Capacitive reactance (X_C): Caused by capacitors in the circuit, given by \( X_C = \frac{1}{2\pi f C} \)

where:

• \( f \) is the frequency of the AC signal
• \( L \) is the inductance
• \( C \) is the capacitance

Impedance in AC Circuits

In AC circuits, impedance plays a crucial role in determining the phase relationship between voltage and current. The phase angle \( \theta \) is given by: \[ \theta = \arctan\left(\frac{X}{R}\right) \]

Applications

Electrical impedance is used in various applications including:

• Impedance matching in radio frequency (RF) circuits to ensure maximum power transfer.
• Bioelectrical impedance analysis (BIA) for measuring body composition.
• Impedance spectroscopy for material characterization.

Related Pages

• Resistance
• Reactance
• Inductance
• Capacitance
• Ohm's law
• Alternating current
• Impedance matching
• Bioelectrical impedance analysis
• Impedance spectroscopy

See Also

• Admittance
• Susceptance
• Conductance