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# Several problems in electricity

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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?

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## 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.
r2/r1 =

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.
q1 =
q2 =

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)

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