A 55.4 ? resistor is connected in series with a 16.2 microF capacitor and a 60 Hz, 140 V source.

a) Find the current in the circuit. Answer in units of mA.

b) What is value of the inductor that must be inserted in the circuit to reduce the current to one half the previous current?

Answer in units of H.

1. Given    V=100V    R=10kΩ    C=10µF    (10 pts)

1. Determine the mathematical expression for v_c

2. Determine the mathematical expression for i_c

3. Computer the capacitor voltage at t=150 ms

4. Computer the capacitor current at t=150 ms

5. Locate the points on the voltage and current curves.

Given an undirected graph G = (V,E), consisting of n vertices and m edges, with each edge labeled from the set {0,1}.

Describe and analyze the worst-case time complexity of an efficient algorithm to find any cycle consisting of edges whose labels alternate 0,1.

Complete this formal proof of Ex(P(x)v~P(x)) from the empty set. NOTE: similar to the rule above when instantiating quantifiers, if you need a random name, always start at the beginning of the alphabet. That is, use a first; only use b if necessary; etc.

Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 1.8×10⁴ m/s when at a distance of 2.6×10¹¹ m from the center of the sun, what is its speed when at a distance of 5.2×10¹⁰ m

v=…..m/s

A 55 kg astronaut who weighs 170 N on a distant planet is pondering whether she can leap over a 4.0-m-wide chasm without falling in.

If she leaps at a 15∘ angle, what initial speed does she need to clear the chasm? v=?

A spring gun fires a bullet of mass m=.04 kg horizontally at a ballistic pendulum apparatus with a mass M=.350. the bullet lodges itself into the pendulum. After collision, the center of mass of the bullet and pendulum rises by .07 meters. What is the approximate initial speed v of the bullet?

For the reaction 2Co3+(aq)+2Cl−(aq)→2Co2+(aq)+Cl2(g). E∘=0.483 V what is the cell potential at 25 ∘C if the concentrations are [Co3+]= 0.456 M , [Co2+]= 0.451 M , and [Cl−]= 4.50×10−2 M and the pressure of Cl2 is PCl2= 2.30 atm ?

Two capacitors are identical, except that one is empty and the other is filled with a dielectric (κ = 4.69). The empty capacitor is connected to a 11.0-V battery. What must be the potential difference across the plates of the capacitor filled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

Prepare a legal Brief for one of the following upcoming Supreme Court Cases:

A) Google LLC v. Oracle America, Inc.
- Does copyright protection extend to a software interface? Does petitioner’s use of a software interface in the context of creating a new computer program constitute fair use?