Show that if E(t) = U cos ωt+V sin ωt where U and V are constants then the steady state current in the RLC circuit shown below
Ip = (ω2RE(t)+(1/C − Lω2)E′(t))/∆
∆ = (1/C − Lω2)2 + R2ω2.
Show that if E(t) = U cos ωt+V sin ωt where U and V are constants...
Show that if E(t) = U cos ωt+V sin ωt where U and V are constants then the steady state current in the RLC is Ip = (ω 2RE(t) + (1/C − Lω2 )E0 (t))/ ∆ , where ∆ = (1/C − Lω2 ) 2 + R 2ω 2 .
6.3 Exercises In Exercises 1-5 find the current in the RLC circuit, assuming that E(t) = 0 fort > 0. 1. R = 3 ohms; L = 1 henrysC = .01 farads; Q. = 0 coulombs, 10 = 2 amperes. 11. Show that if E(t) = U coswt +V sin wt where U and V are constants then the steady state current in the RLC circuit shown in Figure 6.3.1 is w?RE(t) + (1/C - Lw?) E' (t) I where...
Please solve this question The image of the parametrization Ф(u, u)-(a . sin(u) . cos(v), b . sin(u) . sin(v), c . cos(u)) with óくa, 0 < u < π, 0 < v < 2π parametrizes an ellipsoid. a) Show that all the points in the image of Ф satisfy the Cartesian equation of an ellipsoid E 2 b) Show that the image surface is regular at all points c) Write out the integral for its surface area A(E), (Do...
5. Calculate the polarization angles (y, χ) for the wave E(z,t)- f 3 cos(ωt-kz) + 93 cos(wt-k2+ 450) (V/m). Plot E(0, t) to show the polarization state. 5. Calculate the polarization angles (y, χ) for the wave E(z,t)- f 3 cos(ωt-kz) + 93 cos(wt-k2+ 450) (V/m). Plot E(0, t) to show the polarization state.
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
A sinusoidal voltage Δv = 41.0 sin 100t, where Av is in volts and t is in seconds, is applied to a series RLC circuit with L = 150 mH, C = 99.0 μF, and R = 62.0 Ω. (a) What is the impedance of the circuit? (b) What is the maximum current? (c) Determine the numerical value for w in the equation i = Imax sin (ωt - φ). (d) Determine the numerical value for in the equation i = Imax sin (ωt...
A sinusoidal voltage Δv = 45.0 sin(100t), where Δv is in volts and t is in seconds, is applied to a series RLC circuit with L = 140 mH, C = 99.0 µF, and R = 61.0 Ω. (a) What is the impedance (in Ω) of the circuit? ________ Ω (b) What is the maximum current (in A)? _________A (c) Determine the numerical value for ω (in rad/s) in the equation i = Imax sin(ωt − ϕ). _________rad/s (d) Determine...
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
For the following LRC circuit with periodic electric source v(t), find the steady-periodic current in the form isp(t) = I0 sin(ωt − δ), where I0 > 0 and 0 ≤ δ < 2π. (Round numerical values to two decimal places.) R = 20, L = 10, C = 0.01, v(t) = 800 cos(5t)
5. Calculate the polarization angles (y, χ) for the wave E(z,t)- f 3 cos(ωt-kz) + 93 cos(wt-k2+ 450) (V/m). Plot E(0, t) to show the polarization state.