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.

Inductance in DC Circuits

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 (X_{L}) is given by:

Formula:X_{L} = 2πfL

Formula Breakdown:

X_{L}: 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 (X_{L}) is given by:

Formula:Z = √(R² + X_{L}²)

Formula Breakdown:

Z: Impedance (ohms, Ω)

R: Resistance (ohms, Ω)

X_{L}: 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 X_{L} = 2πfL and Z = √(R² + X_{L}²).

X_{L} = 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:X_{L} = 2πfL

Formula Breakdown:

X_{L}: 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 + X_{L}²)

Formula Breakdown:

Z: Impedance (ohms, Ω)

R: Resistance (ohms, Ω)

X_{L}: 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 X_{L} = 2πfL and Z = √(R² + X_{L}²).