See attached for full description of problems.
1. Determine the Laplace transform of ?(t) = + 5e^-4t + 12sin 3t.
2. If v(t) = 10e^-t/3 for some circuit, when does the voltage fall to 37% of its initial value?
3. Let ?(t) = sin2t. What is the Laplace transform of d? / dt ?
4. The charge in a certain capacitor varies as q = 20e^-4t sin 2t C. What is the voltage if the capacitor is 2 F?
5. The charge in a certain inductor varies as q = 2 sin 2t C. What is the voltage if the inductance is 2 H?
6. The current flowing through a 1 H inductor is 10 cos 20t amps. Find the voltage.
7. The current flowing through a 2 F capacitor is i(t) = 5 cos 2t amps. What is the voltage?
8. The current flowing through a 2 H inductor is i(t) = 5 cos 2t amps. What is the voltage?
10. What is the energy in a 2 F capacitor if v(t) = cos2t at t = pi seconds?
11. What is the energy in a 10 H inductor if i(t) = cos2t at t = pi seconds?
12. What kind of damping is associated with ? (t) =(A + Bt) e^wt?
The solution is attached below in two files. the files are ...
The file contains a detailed solution to each of the problems listed below.
Electric fields, Gauss and Coulomb
1. A tiny ball (mass = 0.015 kg) carries a charge of -20 µC. What electric field (magnitude and direction) is needed to cause the ball to float above the ground?
2.At a distance r1 from a point charge, the magnitude of the electric field created by the charge is 284 N/C. At a distance r2 from the charge, the field has a magnitude of 112 N/C. Find the ratio of the distances.
3.Two charges are located on the x axis: q1 = +2.0 µC at x1 = +4.0 cm, and q2 = +2.0 µC at x2 = -4.0 cm. Two other charges are located on the y axis: q3 = +6.0 µC at y3 = +5.0 cm, and q4 = -2.0 µC at y4 = +7.0 cm. Find the net electric field (magnitude and direction) at the origin.
N/C ° (measured counter clockwise from the x axis)
4.A rectangle has a length of 2d and a height of d. Each of the following three charges is located at a corner of the rectangle: +q1 (upper left corner), +q2 (lower right corner), and -q (lower left corner). The net electric field at the (empty) upper right corner is zero. Find the magnitudes of q1 and q2. Express your answers in terms of q.
5.A spherical surface completely surrounds a collection of charges. Find the electric flux through the surface if the collection consists of each of the following.
(a) a single +3.0 10-6 C charge
(b) a single -2.6 10-6 C charge
(c) both of the charges in (a) and (b)View Full Posting Details