electrical engineering ac analysis?

OK.... I blew it on the first try. Here is a second attempt.

The magnitude of the voltage across the inductor (V_l) squared divided by the magnitude of the current (I) squared equals the sum of the squares of the resistive component within the coil (R_l) and the inductive impedance of the coil (2π(f)(L)):

(V_l)²/I² = R_l² + {2π(f)(L)}²

The magnitude of the voltage of across the inductor and resistor (V_l-R) squared divided by the magnitude for the current (I) squared equals the sum of the squares of the resistive components and the inductive components

V_l-R²/I² = (R + R_l)² + {2π(f)(L)}²

Subtracting the first equation from the second will eliminate the inductive component:

(V_l-R² - V_l²)/I² = (R + R_l)² - R_l²

Squaring the first term on the right:

(V_l-R² - V_l²)/I² = R² + 2R(R_l) + R_l² - R_l²

Combining like terms:

(V_l-R² - V_l²)/I² = R² + 2R(R_l)

Substituting V_r/I for R:

(V_l-R² - V_l²)/I² = V_r²/I² + 2(V_r/I)(R_l)

Subtract V_r²/I² from both sides:

(V_l-R² - V_l²)/I² - V_r²/I² = 2(V_r/I)(R_l)

Regrouping:

(V_l-R² - V_l² - V_r²)/I² = 2(V_r/I)(R_l)

Multiply both sides by I:

(V_l-R² - V_l² - V_r²)/I = 2(V_r)(R_l)

Divide both side 2(V_r):

R_l = (V_l-R² - V_l² - V_r²)/{2I(V_r)}

Substituting values for the right-hand side:

R_l = (200² - 150² - 100²)/{2(15)(100)}

R_l = (40000 - 22500 - 10000)/(3000) = 7500/3000 = 2.5 Ω

The resistive component of the coil (R_l) is 2.5 Ω

We may find the inductive component of the coil by returning to the equation:

(V_l)²/I² = R_l² + {2π(f)(L)}²

Subtracting R_l² from both sides:

{2π(f)(L)}² = (V_l)²/I² - R_l²

Take the square root of both side:

2π(f)(L) = sqrt{(V_l)²/I² - R_l²}

L = sqrt{(V_l)²/I² - R_l²}/2π(f)

Substituting values for the right-hand side:

L = sqrt{(150)²/15² - 2.5²}/2π(60)

L = sqrt(100 - 6.25)/120π

L = sqrt(93.75)/120π

L ≈ 2.568 x 10^-2 H

Let's find the phase angle for the impedance of resistor and the inductor:

Θ = tan^-1{sqrt(93.75)/(100/15 + 2.5)} = 46.567°

This means the phase angle for the capacitor and parasitic resistance must have the same phase but opposite in sign:

Θ = -46.567°

The resistive component (R_c) is the magnitude of the voltage (V_c) divided by the magnitude of the current multiplied by (I) multiplied by the cosine of the phase angle:

R_c = (V_c/I)cos(Θ)

Substituting values for the right-hand side:

R_c = (100/15)cos(-46.567) ≈ 4.58 Ω

The capacitive component (-1/{2π(f)C}) is equal the magnitude of the voltage (V_c) divided by the the magnitude of the current multiplied by the sine of the phase angle:

-1/{2π(f)C} = (V_c/I)sin(Θ)

2π(f)C = -I/{(V_c)sin(Θ)}

C = -I/{2π(f)(V_c)sin(Θ)}

Substituting values for the right-hand side:

C = -15/{120π(100)sin(-46.567)} ≈ 5.479 x 10^-4 F

Check:

The impedance of the inductor is:

sqrt{2.5² + (120π(2.568 x 10^-2)²} ≈ sqrt(100) = 10

The impedance of the capacitor is:

sqrt{4.58² + (1/{120π(5.479 x 10^-4)})²} ≈ 20/3

When multiplied by 15 A, both of these values give the respective voltage. Therefore, this checks.

the position I stay, to grow to be a qualified engineer, calls for a 4 3 hundred and sixty 5 days bachelor's degree. that is available at Universities, no longer faculties. Judging by employing your concern record, you're on target for a B.Eng. perchance the position you stay, faculties do furnish B.Eng stages. typically, my BEng classes were 80% calculus, and 20% circuit theory - yet, the calculus became disguised with names like "EM propagation", "PDEs", "Vector diagnosis" and "DSP". reckoning on who, how, and the position, each and each concern is taught, will impression how confusing they look. My class at my college discovered PDEs (partial differential eqns) and EM (electromagnetics) to be the most calculus huge, and therefore, maximum problematical. administration structures also use Laplace, this can be a technique correct to calculus. in case you are able to spend the summer season sipping a beverage in a unmarried hand, and your PDE or CS texts in the different in a wide-spread chair or hammock, comfortably surfing with the help of the fabric before it truly is forcibly put in in September, you'll do nicely. playstation : there is not any damage, and no shame, in spreading your classes out over an more advantageous semester. in case you do 5-6 classes a semester, really of 8, think about a million more advantageous semester, yet, you are able to then tolerate the p.c.. easier, savour somewhat social life, and perchance carry an element time interest to offset guidance, or chew into any student loans gathering. only double examine along with your branch head so that you do not omit pre-standards, and so that you protect "tutorial forex" - you do not favor to spread them out over 8 years (i exaggerate), in basic words to be certain the before ones have 'expired' and now no longer count number in the route of your degree.