Electrical Engineering Answers

Nichrome ribbon resistor elements each has a resistance of 1Ω. The element is made from sheet of nichrome alloy, 0.025 cm thick. If the width of the ribbon is 0.3 cm, what length is required per element? Assume specific resistance of nichrome alloy to be 109 micro Ω-cm. (include step-by-step procedures)

Find the approximation of the jaobi's method and gauss-seidel method for the following linear system, using 𝑥(0) = 0 :

10𝑥1 - 𝑥2 = 9,

-𝑥1+10𝑥2 - 2𝑥3 = 7,

-2𝑥2 + 10𝑥3 = 6.

Use the Euler's method and Runge-Kutta method for systems to approximate y1(0.72+0.72), y2(0.72), y2(0.72+0.72) of the following systems of first-order differential equations:

dy1/dx=y1-y2+2, y1(0)= -1

dy2/dx= -y1+y2+4x

y2(0)=0 ; 0 ≤ x ≤ 2

Three resistors of 10, 12 and "x" ohms, respectively are connected in parallel across a constant current source of 8A. Determine "x" if this resistor draws 2.5 A.

Use the classical Runge-Kutta method of order four to solve the initial value problem y' = y-t^2 +1, y(0) =05 and 0 ≤ t ≤ 3 to approximate y(0.72), y(0.72+0.72), y(0.(3×72)), y(0.(4×72)).

Use the classical Runge-Kutta method of order two, Mid-point method, Ralston's method to solve the initial value problem y' =y - t^2 +1, y(0) = 0.5 and 0 ≤ t ≤ 3 to approximate y(0.72), y(0.72+0.72), y(0.(3×72 )), y(0.(4×72)).

Use Euler's method and modified Euler's method to solve the initial value problem dy/dx = 1+x/1+y,

y(1) = 2 and 1≤ x ≤ 4 to approximate y(1.72), y(1.72+0.72), y(1.(3×72)), y(1.(4×72)),

The exact solution is given by y(x)=x+ 1/1-x . Determine the crror at cach step.