4.2.2 What is an RC Circuit?

Recall that the capacitance is defined as the proportionality constant between the total charge accumulated by a capacitor and the voltage difference across the circuit

Q = C△V (4.2)

In this equation, the charge Q is expressed in Coulomb (C), the voltage △V, in volts (V) and the capacitance C in farads (F).

In this lab you will study both the charging and discharging process of an RC circuit. During the charging process, an electrical EMF source accumulates charges on each side of the parallel plate capacitor. During the discharging process, the capacitor releases all its charges into the circuit (which now does not contain the battery). Capacitors charge and discharge exponentially in time. During the discharge of a capacitor, the instantaneous voltage △Vc between the ends of the capacitor also drops and is given by △Vс = △Vmax*e^(-t/τ) (4.3) where △Vmax is the maximum voltage across the capacitor, i.e. the voltage to which thecapacitor was initially charged, t is the time and τ is the time constant given by τ= Req*Ceq (4.4) where Req and Ceq are, respectively, the equivalent resistance and capacitance to which we can reduce the circuit. Although the theoretical discharge time is in nite, in practice we consider that the discharge is over when the voltage at the bounds of the capacitor is at 1% of its maximal value.

Answer the following questions in the Results section: Assuming the voltage, when completely charged, is set to V₀ = 1 and by considering the variables τ for time constant and t for time, what are the equations for of charging and discharging? Support your answer by physical arguments

A rocket takes off vertically from the launchpad with no initial velocity but a constant upward acceleration of 2.25 m/s2 . At 15.4s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity (free fall). a) What is the maximum height the rocket will reach above the launchpad? b) How fast is the rocket moving at the instant before it crashes onto the launchpad? c) How much longer after the engines fail does it take for the rocket to crash on the launchpad?

1.   A boy pushes a load of 1260 N at a constant speed up a 25° inclined plane onto a platform 1.0 m high. If the boy’s maximum force is 300 N parallel to the plane and the coefficient of kinetic friction is 0.4, what must be the length of the plane?

1. Boltzmann statistics are used to find the distribution or distribution of the velocity of Inert gas at any temperature. If D (v) is the velocity distribution of inert gas at T, then the probability that atoms (or Molecules) of inert gas have velocity in the dv range is equal to D (v) dv, where
D (v) dv = 4π (m / 2πkT) ^ 3⁄2 (v ^ 2) e ^ (- mv2⁄2kT) dv

2.1 Draw the graph between D (v) and v when the inert gas has a temperature of 1000 K (Recommended: Use a program such as Mathematica) to explain. Graph style
2.2 In the Thermosphere atmosphere, which is 100 - 150 km above the earth, the temperature is around 1000 K. Find the probability
Is that the nitrogen gas molecules will escape from gravity. In which the molecules must be faster than the velocity From the earth's surface, which is equal to 11 km / s (recommended: for integration D (v) dv, use the program For example Mathematica)
2.3 The lunar surface velocity is 2.4 km / s. Find the probability that the nitrogen gas molecules will escape from the force. Gravity of the moon And explain that Why does the moon have no atmosphere? (Recommended: set the temperature of the moon's surface to equal1000 K)

Two wires separated by 2 meters are carrying current in the same direction. One carries a current of 2 amps and the other carries a current of 3 amps. For the following, show all work starting with the equations at the top of the first page and/or explain your reasoning. Do NOT simply write down a formula specifically derived for this problem.

1. Find the force on the wire carrying the 3-amp current. In which direction does it point?

2. Find the force on the wire carrying the 2-amp current. In which direction does it point?

3. Will the wires attract each other or repel?

A charge q1 of +3.0 x10^-6C is held at (-12, 0) (cm) . Another charge q2 of the same magnitude is held at (12,0). The third charge q3 is held at (0,8) = -6x10^16C

a) What is the magnitude of the net force on charge q1 and q2

b) If q3 were to be released what direction and angle will it move in

c) At what point on the plane would a charge q4 of +15x 10^-6 be placed so that net force is 0

6.) A 'Newton's Cradle' consists of 7 identical metal balls which are free to swing back and forth. When two are pulled back and then released, they stop after colliding elastically with the other 5 balls. The two balls on the other end then swing upwards with the same speed as the first two balls. Using the conservation of momentum and mechanical energy, explain why only two balls move afterwards. Use words and/or equations to explain your answer.

The diffusion coefficient of a large protein molecule is found to be 2.2×10^-13 m²/s in the water at 20∘C. Assuming it is spherical with a density of 1.3×10³ kg/m³, compute its molar mass.

Does the gravitational force of a satellite changes depending on the orbit it follows

A large cyclotron directs a beam of He++ nuclei onto a target with a beam current of 0.245 mA.

(a) How many He++ nuclei per second is this? He++ nuclei/s

(b) How long (in s) does it take for 1.35 C to strike the target? s

(c) How long (in s) before 1.20 mol of He++ nuclei strike the target? s

Please show step by step with legible writing. Thank you

n object with mass 100 kg moved in outer space. When it was at location <6, -26, -7> its speed was 6.0 m/s. A single constant force <230, 310, -120> N acted on the object while the object moved from location <6, -26, -7> m to location <12, -22, -11> m. Then a different single constant force <100, 260, 120> N acted on the object while the object moved from location <12, -22, -11> m to location <16, -27, -6> m. What is the speed of the object at this final location? final speed = m/s

A tennis ball is lobbed (from very close to the ground) at a speed of 11.5 m/s and an angle of 47.9 degrees to the horizontal. (a) Find the horizontal distance traveled by the ball (the range) (b) At what other angle will one obtain the same range? (c) Which angle gives the highest point attained by the ball and what is this maximum height? (In all cases ignore air resistance)

A small metal sphere, A, carrying a charge of +15.0μC is at the origin. An identical sphere, B, carrying a charge of -18.0μC is at~ xB= 4.0ˆi cm and a third sphere, C,carrying +25.0μC is at~x C= 3.0ˆj cm.

(a) Find the total electrical force exerted on sphere A.

(b) Let us view sphere A as a probe charge which we are using to measure the field due to spheres B and C. Use your result from part b) to find the electric field (note that this is a vector) at the origin.

(c) Sphere A is released so that it is free to move. It has a mass of 5.0 g and no forces other than the electrostatic forces found in a) act on it. What is its acceleration at the instant of release?

(d) A short time later will your answer from c) still be the correct acceleration for sphere A?

(e) Spheres B and C are touched together and then returned to their original locations.Sphere A is also returned to its original location. Now what is the force on sphere A?

Hello, I have three questions.

1. What happens to the amount of air resistance on your car as you drive faster?

2. When will an object falling through air reach terminal velocity?

3. What is the net force and acceleration of an object that has reached terminal velocity?