Deduce an equation U = 1 2 LI 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power , rate of doing work) = ε I dt ( power = voltage (emf) x current ) But ε = - L di dt ( in case of an inductor) therefor dw = L dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

Deduce an equation U = 1 2 LI 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power , rate of doing work) = ε I dt ( power = voltage (emf) x current ) But ε = - L di dt ( in case of an inductor) therefor dw = L dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

Deduce an equation U = 1 2 L I 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power, rate of doing work ). = ε I dt (power = voltage (emf) x current). But ε = - L di dt (in case of an inductor). therefor dw = LI dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

Deduce an equation U = 1 2 L I 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power, rate of doing work ). = ε I dt (power = voltage (emf) x current). But ε = - L di dt (in case of an inductor). therefor dw = LI dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2018>Q 6

MEDIUM

12th Gujarat Board

IMPORTANT

Earn 100

Deduce an equation $U = \frac{1}{2} {LI}^{2}$ for an inductor.

Important Questions on Alternating Current

HARD

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2018>Q 7

Using the equation

$\frac{di}{dt} + \frac{R}{L} i + \frac{1}{LC} \int idt = \frac{V_{m}}{L} e^{iωt}$ . for L-C-R circuit, obtain an equation for the complex current $' i'$ and explain its different terms in the equation. Hence obtain the equation for real current $' i'$