A series ac circuit contains a 210 Ω resistor, a 20.0 mH inductor, a 3.30 μF capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s . 1)What is the power factor of this circuit? 2)Find the average power delivered to the entire circuit. 3)What is the average power delivered to the resistor, to the capacitor, and to the inductor?

A dielectric-filled parallel-plate capacitor has plate area A = 25.0 cm2 , plate separation d = 9.00 mm and dielectric constant k = 2.00. The capacitor is connected to a battery that creates a constant voltage V = 12.5 V . Throughout the problem, use ϵ0 = 8.85×10⁻¹² C2/N⋅m2 .

PART A:

U₁ was found:

PART B:

The dielectric plate is now slowly pulled out of the capacitor, which remains connected to the battery. Find the energy U2 of the capacitor at the moment when the capacitor is half-filled with the dielectric.

Express your answer numerically in joules.

PART C:

The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U3.

Express your answer numerically in joules.

PART D:

In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on the dielectric?

Express your answer numerically in joules.

Two small nonconducting spheres have a total charge of Q=Q1+Q2= 90.0 μC , Q1<Q2. When placed 31.0 cm apart, the force each exerts on the other is 13.0 N and is repulsive.

Part A: What is the charge Q1?

Part B: What is the charge Q2?

Part C: What would Q1 be if the force were attractive?

Part D: What would Q2 be if the force were attractive?

In areas of enhanced heat flow, geothermal heating can be used to supply heating to homes, either by using ground water directly or by placing a water reservoir at depth. In Iceland, where the average temperature over the year is 4.6ºC, the geothermal flux can be as high as 300 mW m-2.

(a)

If you wanted to be able to supply a home with indoor temperature at 25ºC and water at a temperature of 55ºC, how deep would your reservoir need to be?

(b)

Why might Iceland have such a high geothermal flux compared to other areas?

(c)

Does high geothermal flux accelerate the melting of ice sheets, why or why not?

A convex mirror has a focal length of -58.0 cm. A 12.0-cm-tall object is located 58.0 cm in front of this mirror. Determine the (a) location and (b) size of the image.

How is a panel study different from a pilot study? (8-10 sentences)

light travels from air through two layers with index of refraction n1 and n2, respectively. If upon entering each layer light loses 10% of its velosity, what is the index of refraction n2

3.) To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance). Assume all values are accurate to three significant digits. (Assume the density of air is 1.21 kg/m³.)

A.) What is the magnitude of drag force (in N) at 58 km/h and 116 km/h for a Toyota Camry? (Drag area is 0.70 m², and drag coefficient is 0.28.)

B.) What is the magnitude of drag force (in N) at 58 km/h and 116 km/h for a Hummer H2? (Drag area is 2.44 m², and drag coefficient is 0.64.)

How much heat is required to change a 30.2 g ice cube from ice at -13.8°C to water at 23°C? (if necessary, use c_ice=2090 J/kg°C and c_steam= 2010 J/kg°C)

How much heat is required to change a 30.2 g ice cube from ice at -13.8°C to steam at 120°C?

Which of the following best indicates the components of a vector that measures 30 m at 135°?

a)<21, 21> m

b)<-21, 21> m

c)<21, -21> m

d)<-21, -21> m

A student runs off of a diving platform with a speed of 2.5 m/s and hits the water 0.8 seconds later. What is the height of the platform?

Vector A has components A = <-2, 5> m/s and vector B has components B = <6, -2> m/s. What is the magnitude of vector C if C = A + B?

A student fires a bullet horizontally from a gun. Which statement is most accurate?

Which of the following is an example of a vector measurement?

A person driving through a field has velocity components that are 30 m/s west and 20 m/s south. What is the approximate direction of the overall velocity?

A student kicks a ball that is initially at rest on the ground. The ball leaves the student's foot with some velocity v at an angle θ. When the ball is at its maximum height, which statement is most accurate?

A proton has an initial velocity of 7.6 × 106 m/s in the horizontal direction. It enters a uniform electric field of 8800 N/C directed vertically.

a) Ignoring gravitational effects, find the time it takes the proton to travel 0.127 m horizontally. The mass of the proton is 1.6726 × 10−27 kg and the fundamental charge is 1.602 × 10−19 C . Answer in units of ns.

b)What is the vertical displacement of the proton after the electric field acts on it for that time? Answer in units of mm.

c) What is the proton’s speed after being in the electric field for that time? Answer in units of km/s.

An electron starts from rest 27.0 cm from a fixed point charge with Q = -8.00 nC .

How fast will the electron be moving when it is very far away?

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Many chemical reactions release energy. Suppose that at the beginning of a reaction, an electron and proton are separated by 0.135 nm , and their final separation is 0.101 nm .

How much electric potential energy was lost in this reaction (in units of eV)?

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A 0.21-F capacitor is desired. What area must the plates have if they are to be separated by a 3.2-mm air gap?

Robert Millikan is famous for his experiment which demonstrated that electric charge is discrete, or quantized. His experiment involved measuring the terminal velocities of tiny charged drops of oil in air between two plates with a known voltage applied. He timed hundreds of them traveling both up and down in order to mathematically rule out the effects of gravity and drag, since he had no way of measuring mass or diameter. His results showed that charge comes only in integer multiples of 1.6 10 19C. This is called the elementary charge. It is the charge on both electrons, negative, and protons, positive.
1. a. Where does charge excess charge reside on an object? Why?
b. Where is electric charge more concentrated on irregularly shaped objects?
c. How do lightning rods work?
d. Why does a stream of water bend toward a charged object?
e. What are the three methods of charging an object?

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.20 s later. You may ignore air resistance.

A) If the height of the building is 20.7 m , what must the initial speed be of the first ball if both are to hit the ground at the same time?

B) Consider the same situation, but now let the initial speed v0 of the first ball be given and treat the height h of the building as an unknown. What must the height of the building be for both balls to reach the ground at the same time for v0 = 8.65 m/s .

C) If v0 is greater than some value vmax, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmax.

D) If v0 is less than some value vmin, a value of h does not exist that allows both balls to hit the ground at the same time. Solve for vmin.

) (Take eastward as the positive direction) Zachary, who is a runner, runs 8.30m/s westward for 12.0s. Zachary then turns around and runs 50.0m eastward toward the starting point in 30.0s. What is the Zachary’s a) total displacement b) total distance traveled c) explain the difference in your values for parts (a) and (b) d) average speed for the entire run e) average velocity for the entire run f) explain the difference in your values for parts (d) and (e)