inductance

inductance

1. What Inductance Is

Inductance ($L$, henry $H$) = property to oppose change in current via induced emf from changing magnetic flux (Faraday). For a coil with $N$ turns, flux linkage

where $φ$ = flux per turn. So

SI $H = V·s/A$.

Self-inductance: emf induced in same coil:

(Lenz: opposes change). Mutual inductance $M$ (next topic) is between coils.

2. Nature — Passive, Energy Storage

• Passive (absorbs, not generates), but stores energy in magnetic field:

(vs capacitor $1/2 C V²$ in electric field).

• Linear if $μ$ constant (air-core); non-linear with iron core (saturation, $L$ varies with $I$).
• DC: $L$ is short at steady DC (0 resistance, $e=0$ if $dI/dt=0$); at transient and AC it shows reactance

(Ω), voltage leads current by $90°$.

3. Factors

For solenoid $N$ turns, length $l$, area $A$, $μ=μ_0 μ_r$:

For $μ_r$ iron ~1000–10000 ⇒ $L$ large. Air-core small.

4. Worked Examples

(a) Solenoid N=1000, l=0.1 m, A=1e-4 m², μ0=4πe-7 ⇒ L=4πe-7·1e6·1e-4/0.1=1.26e-3 H=1.26 mH (air) ✓
    With iron μr=1000 ⇒ 1.26 H ✓

(b) L=10 mH, dI/dt=100 A/s ⇒ e=-1 V ✓

(c) Energy in L=1 mH at I=2 A: W=0.5·1e-3·4=2 mJ ✓

(d) Need to limit di/dt? Inductor blocks high-frequency: X_L=2π·1k·10mH≈62.8 Ω

5. Exam Points

• Define $L=Nφ/I$, $H$, $e=-L dI/dt$, $W=½LI²$ — 5 marks, very frequent.
• Give $X_L=ωL$ and phase lead — 3-5 marks, frequent.
• Formula $L=μN²A/l$ — 5 marks, frequent.
• Distinguish linear vs non-linear (air vs iron) — 3 marks.