4.77 Augment the rectifier circuit of Problem 4.70 with a capacitor chosen to provide a peak-to-peak ripple voltage of (i) 10% o
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Answer:
Explanation:
Given that,
The radius of sphere, r = 5 cm = 0.05 m
Net charge carries, q = 7.5 µC = 7.5 × 10⁻⁶ C
We need to find the surface charge density on the sphere. Net charge per unit area is called the surface charge density. So,
So, the surface charge density on the sphere is .
The question is missing some parts. Here is the complete question.
An ideal gas is contained in a vessel at 300K. The temperature of the gas is then increased to 900K.
(i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of , (d) a factor of 1, or (e) a factor of
?
Using the same choices in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a colision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas.
Answer: (i) (b) a factor of 3;
(ii) (c) a factor of ;
(iii) (c) a factor of ;
(iv) (c) a factor of ;
(v) (e) a factor of 3;
Explanation: (i) Kinetic energy for ideal gas is calculated as:
where
n is mols
R is constant of gas
T is temperature in Kelvin
As you can see, kinetic energy and temperature are directly proportional: when tem perature increases, so does energy.
So, as temperature of an ideal gas increased 3 times, kinetic energy will increase 3 times.
For temperature and energy, the factor of change is 3.
(ii) Rms is root mean square velocity and is defined as
Calculating velocity for each temperature:
For 300K:
For 900K:
Comparing both veolcities:
For rms, factor of change is
(iii) Average momentum change of molecule depends upon velocity:
q = m.v
Since velocity has a factor of and velocity and momentum are proportional, average momentum change increase by a factor of
(iv) Collisions increase with increase in velocity, which increases with increase of temperature. So, rate of collisions also increase by a factor of .
(v) According to the Pressure-Temperature Law, also known as Gay-Lussac's Law, when the volume of an ideal gas is kept constant, pressure and temperature are directly proportional. So, when temperature increases by a factor of 3, Pressure also increases by a factor of 3.
Starting from the angular velocity, we can calculate the tangential velocity of the stone:
Then we can calculate the angular momentum of the stone about the center of the circle, given by
where
m is the stone mass
v its tangential velocity
r is the radius of the circle, that corresponds to the length of the string.
Substituting the data of the problem, we find
Then we can calculate the angular momentum of the stone about the center of the circle, given by
where
m is the stone mass
v its tangential velocity
r is the radius of the circle, that corresponds to the length of the string.
Substituting the data of the problem, we find