Inductance is the property of an electrical conductor that opposes a change in current. It is measured in henries (H) and is influenced by factors such as the number of turns in a coil, the cross-sectional area, and the core material.
In DC circuits, inductance primarily affects the transient response of the circuit. When the current through an inductor changes, it induces a voltage that opposes the change. The energy stored in the inductor is given by:
Formula:W = 0.5 × L × I²
Formula Breakdown:
W: Energy stored (joules, J)
L: Inductance (henries, H)
I: Current (amperes, A)
Example Calculation:
Task: Calculate the energy stored in an inductor with an inductance of 2 H and a current of 3 A.
Solution: Use the formula W = 0.5 × L × I².
W = 0.5 × 2 H × (3 A)² = 9 J
Inductance in AC Circuits
In AC circuits, inductance causes a phase shift between voltage and current. The inductive reactance (XL) is given by:
Formula:XL = 2πfL
Formula Breakdown:
XL: Inductive reactance (ohms, Ω)
f: Frequency (hertz, Hz)
L: Inductance (henries, H)
The impedance (Z) in an AC circuit with resistance (R) and inductive reactance (XL) is given by:
Formula:Z = √(R² + XL²)
Formula Breakdown:
Z: Impedance (ohms, Ω)
R: Resistance (ohms, Ω)
XL: Inductive reactance (ohms, Ω)
Example Calculation:
Task: Calculate the inductive reactance and impedance of a circuit with an inductance of 0.1 H, a frequency of 60 Hz, and a resistance of 10 Ω.
Solution: Use the formulas XL = 2πfL and Z = √(R² + XL²).
XL = 2π × 60 Hz × 0.1 H ≈ 37.7 Ω
Z = √(10 Ω)² + (37.7 Ω)² ≈ 38.9 Ω
Inductance in Three-Phase Systems
In three-phase systems, inductance affects the impedance of each phase. The calculations for inductive reactance and impedance are similar to single-phase systems but applied to each phase.
Formula:XL = 2πfL
Formula Breakdown:
XL: Inductive reactance (ohms, Ω)
f: Frequency (hertz, Hz)
L: Inductance (henries, H)
The total impedance (Z) in each phase of a three-phase system is given by:
Formula:Z = √(R² + XL²)
Formula Breakdown:
Z: Impedance (ohms, Ω)
R: Resistance (ohms, Ω)
XL: Inductive reactance (ohms, Ω)
Example Calculation:
Task: Calculate the inductive reactance and impedance in each phase of a three-phase system with an inductance of 0.2 H, a frequency of 50 Hz, and a resistance of 15 Ω.
Solution: Use the formulas XL = 2πfL and Z = √(R² + XL²).