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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.
Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring
Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle
Derivation Of The Area Of An Ellipse
Derivation Of Volume Of A Cylinder
Derivation Of Volume Of A Sphere
Derivation Of Volume Of A Cone
Derivation Of Volume Of A Torus
Derivation Of Volume Of A Paraboloid
Volume Obtained By Revolving The Curve y = x2 About The X Axis
Single Variable Functions
Absolute Value Functions
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Real Numbers
Vector Spaces
Equation Of The Ascent Path Of An Airplane
Calculating Capacity Of A Video Adapter Board Memory
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Boolean Algebra - Logic Functions
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Introduction To Group Theory
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Production Schedule That Maximizes Profit Given Constraint Equation
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Fourier Series
Derivation Of Heat Equation For A One-Dimensional Heat Flow
Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Periodic Table
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
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Molecular Orbital Theory
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