Impedance in DC Circuits
In DC circuits, impedance is simply the resistance, as inductive and capacitive reactance are zero at zero frequency.
Formula: Z = R
Formula Breakdown:
- Z: Impedance (ohms, Ω)
- R: Resistance (ohms, Ω)
Example Calculation:
- Task: Calculate the impedance of a DC circuit with a resistance of 10 Ω.
- Solution: Use the formula Z = R.
- Z = 10 Ω
Impedance in AC Circuits
In AC circuits, impedance is more complex due to the presence of inductive and capacitive reactance. The total impedance (Z) is given by:
Formula: Z = √(R² + (XL - XC)²)
Formula Breakdown:
- Z: Impedance (ohms, Ω)
- R: Resistance (ohms, Ω)
- XL: Inductive reactance (ohms, Ω)
- XC: Capacitive reactance (ohms, Ω)
Inductive Reactance (XL) Formula: XL = 2πfL
Capacitive Reactance (XC) Formula: XC = 1 / (2πfC)
Example Calculation:
- Task: Calculate the impedance of an AC circuit with a resistance of 10 Ω, inductance of 0.1 H, capacitance of 100 μF, and a frequency of 60 Hz.
- Solution: Use the formulas XL = 2πfL, XC = 1 / (2πfC), and Z = √(R² + (XL - XC)²).
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- XL = 2π × 60 Hz × 0.1 H ≈ 37.7 Ω
- XC = 1 / (2π × 60 Hz × 100 × 10^-6 F) ≈ 26.5 Ω
- Z = √(10 Ω)² + (37.7 Ω - 26.5 Ω)² ≈ 15.1 Ω
Impedance in Three-Phase Systems
In three-phase systems, impedance affects the impedance of each phase. The calculations for impedance are similar to single-phase systems but applied to each phase.
Formula: Z = √(R² + (XL - XC)²)
Formula Breakdown:
- Z: Impedance (ohms, Ω)
- R: Resistance (ohms, Ω)
- XL: Inductive reactance (ohms, Ω)
- XC: Capacitive reactance (ohms, Ω)
Example Calculation:
- Task: Calculate the impedance in each phase of a three-phase system with a resistance of 15 Ω, inductance of 0.2 H, capacitance of 50 μF, and a frequency of 50 Hz.
- Solution: Use the formulas XL = 2πfL, XC = 1 / (2πfC), and Z = √(R² + (XL - XC)²).
-
- XL = 2π × 50 Hz × 0.2 H ≈ 62.8 Ω
- XC = 1 / (2π × 50 Hz × 50 × 10^-6 F) ≈ 63.7 Ω
- Z = √(15 Ω)² + (62.8 Ω - 63.7 Ω)² ≈ 15.03 Ω