﻿ Energy Stored In A Magnetic Field And Incremental Inductance

Magnetic Field Energy And Incremental Inductance

Strings (SiPjAjk) = S7P3A32     Base Sequence = 12735     String Sequence = 12735 - 3 - 32

Expressions Of Pj Problems
Magnetic Field Energy And Incremental Inductance
Math Figure 16.2 shows the i - λ characteristics of an iron-core inductor:
(a) Calculate the energy and incremental inductance for i = 1 A.
(b) Given that the sinusoidal current i(t) = 0.5sin2πt and coil resistance is 2Ω, calculate the voltage across the terminals of the inductor.

The string:
S7P3A32 (Force - Push).
The math: Pj Problem of interest is of type force. Energy, power and voltage problems are force problems
Energy for i = 1A (λ = 3), is:
Wm = Area bounded by λ = 3; λ = 0 and the characteristics curve
So, Wm = area of trapezoid + area of triangle
So, Wm = 1/2(3-2)(1 + 0.5) + 1/2(2)(0.5) = 0.75 + 0.5 = 1.25 J.

Incremental inductance, LΔ = (di/dλ)-1
So, LΔ = inverse of slope of curve at i= 1 A (λ = 3)
So, LΔ = [(1-0.5)/3-2]-1 = (0.5)-1 = 2 H.

Voltage across terminal of inductor, v = iR + LΔ(di/dt)
So, v = 2(0.5sin2πt) + 2(0.5)(2π)cos2πt = sin2πt + 2πcos2πt. The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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