Energy Stored In A Magnetic Field And Incremental Inductance

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Energy Stored In A Magnetic Field And Incremental Inductance

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**:

S_{7}P_{3}A_{32} (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:

W_{m} = Area bounded by λ = 3; λ = 0 and the characteristics curve

So, W_{m} = area of trapezoid + area of triangle

So, W_{m} = 1/2(3-2)(1 + 0.5) + 1/2(2)(0.5) = 0.75 + 0.5 = 1.25 J.

Incremental inductance, L_{Δ} = (di/dλ)^{-1}

So, L_{Δ} = inverse of slope of curve at i= 1 A (λ = 3)

So, L_{Δ} = [(1-0.5)/3-2]^{-1} = (0.5)^{-1} = 2 H.

Voltage across terminal of inductor, v = iR + L_{Δ}(di/dt)

So, v = 2(0.5sin2πt) + 2(0.5)(2π)cos2πt = sin2πt + 2πcos2πt.

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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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