What is Self inductance? Derive an expression for the self inductance of a solenoid. Also write the factors affecting it.

**OR**

What is a Transformer? Describe its principle and the different types of energy losses in it.

Question

What is Self inductance? Derive an expression for the self inductance of a solenoid. Also write the factors affecting it.

**OR**

What is a Transformer? Describe its principle and the different types of energy losses in it.

Accepted Answer

>

> [!TLDR]
> Self-inductance quantifies a coil's opposition to changing current, and for a solenoid it depends on turns density, area, and core material; a transformer transfers power via mutual induction, with real transformers losing some energy to resistive and magnetic-core effects.
>
> **Self-inductance:** Self-inductance is the property of a coil (or circuit) by virtue of which it opposes any change in the current flowing through it, by inducing an emf in itself. It is defined through the relation $\Phi = LI$ (flux linkage proportional to current) or equivalently by the induced emf $\varepsilon = -L\,dI/dt$, where $L$ is the coefficient of self-inductance, measured in henry (H).
>
> **Derivation for a long solenoid:** Consider a solenoid of length $l$, cross-sectional area $A$, with $N$ total turns (so $n = N/l$ turns per unit length), carrying current $I$. The magnetic field inside a long solenoid is (assumed uniform):
> $$B = \mu_0 n I$$
> The magnetic flux linked with each turn is $B\cdot A = \mu_0 n I A$, and the total flux linkage with all $N = nl$ turns is:
> $$\Phi = N \cdot BA = (nl)(\mu_0 nI)(A) = \mu_0 n^2 A l\, I$$
> Comparing with $\Phi = LI$:
> $$L = \mu_0 n^2 A l = \frac{\mu_0 N^2 A}{l}$$
> If the solenoid has a magnetic core of relative permeability $\mu_r$, this becomes $L = \mu_0\mu_r n^2 Al$.
>
> **Factors affecting self-inductance:** (1) number of turns $N$ (or turns density $n$) — $L\propto N^2$; (2) cross-sectional area $A$ of the solenoid — $L\propto A$; (3) length $l$ of the solenoid; (4) permeability of the core material — inserting a ferromagnetic (high-$\mu_r$) core greatly increases $L$.
>
> **OR — Transformer:** A transformer is a static device used to change (step up or step down) an alternating voltage, consisting of two coils — a primary and a secondary — wound on a common laminated iron core. Its principle is mutual induction: an alternating current in the primary coil produces a continuously changing magnetic flux in the cor

Q.What is Self inductance? Derive an expression for the self inductance of a solenoid. Also write the factors affecting it. OR What is a Transformer? Describe its principle and the different types of energy losses in it.

Concept understanding — Self-Inductance of a Solenoid

Self-Inductance of a Solenoid: From Intuition to Formula

Why does a solenoid oppose current changes?

The precise statement

Where does $L = \mu_0 n^2 A l$ come from?

What does a larger $L$ mean?

Q.What is Self inductance? Derive an expression for the self inductance of a solenoid. Also write the factors affecting it. OR What is a Transformer? Describe its principle and the different types of energy losses in it.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days