Question: The following questions refer to the circuit shown in Figure 18.114, consisting of two flashlight batteries and two Nichrome wires of different lengths and different thicknesses as shown (corresponding roughly to your own thick and thin Nichrome wires).
The thin wire is 50 cm long, and its diameter is 0.25 mm. The thick wire is 15 cm long, and its diameter is 0.35 mm. (a) The emf of each flashlight battery is 1.5 V. Determine the steady-state electric field inside each Nichrome wire. Remember that in the steady state you must satisfy both the current node rule and energy conservation. These two principles give you two equations for the two unknown fields. (b) The electron mobility
in room-temperature Nichrome is about . Show that it takes an electron 36 min to drift through the two Nichrome wires from location B to location A. (c) On the other hand, about how long did it take to establish the steady state when the circuit was first assembled? Give a very approximate numerical answer, not a precise one. (d) There are about mobile electrons per cubic meter in Nichrome. How many electrons cross the junction between the two wires every second?
The value of the electric field in the thin wire is and electric field in the thick wire is .
The thin wire is 50 cm long and the diameter is 0.25 mm.
The flashlight battery is 1.5 V.
Consider the expression for the current in the metal wire as:
Consider the formula for the drift sped of the mobile electrons is proportional to the magnitude of the electric field as:
Here, u is the proportionality constant and the is called the electrons mobility.
Consider from equation (1) and (2), the equation for the current in the wire is derived as:
Determine the area of the thin nichrome wire as:
Determine the area of thick nichrome wire as:
Consider the emf of each battery is 1.5 V and since there are two batteries then the total emf is:
Consider the KCL equation for the steady state. In this case the current in the thick and the thin wire must be equal.
Consider the loop equation as follows:
Substitute the values and solve as:
A ball of mass 0.4 kg flies through the air at low speed, so that air resistance is negligible.
(a) What is the net force acting on the ball while it is in motion?
(b) Which components of the ball's momentum will be changed by this force?
(c) What happens to the x component of the ball's momentum during its flight?
(d) What happens to the y component of the ball's momentum during its flight?
(e) What happens to the z component of the ball's momentum during its flight?
(f) In this situation, why is it legitimate to use the expression for average y component of velocity, , to update the y component of position?
Here are questions about human diet. (a) A typical candy bar provides 280 calories (one “food” or “large” calorie is equal to ). How many candy bars would you have to eat to replace the chemical energy you expend doing 100 sit-ups? Explain your work, including any approximations or assumptions you make. (In a sit-up, you go from lying on your back to sitting up.) (b) How many days of a diet of 2000 large calories are equivalent to the gravitational energy difference for you between sea level and the top of Mount Everest, 8848 m above sea level? (However, the body is not anywhere near 100% efficient in converting chemical energy into change in altitude. Also note that this is in addition to your basal metabolism.)
We will consider the possibility that a free electron acted on by an electric field could gain enough energy to ionize an air molecule in a collision. (a) Consider an electron that starts from rest in a region where there is an electric field (due to some charged objects nearby) whose magnitude is nearly constant. If the electron travels a distance and the magnitude of the electric field is , what is the potential difference through which the electron travels? (Pay attention to signs: Is the electron traveling with the electric field or opposite to the electric field?) (b) What is the change in potential energy of the system in this process? (c) What is the change in the kinetic energy of the electron in this process? (d) We found the mean free path of an electron in air to be about , and in the previous question you calculated the energy required to knock an electron out of an atom. What is the magnitude of the electric field that would be required in order for an electron to gain sufficient kinetic energy to ionize a nitrogen molecule? (e) The electric field required to cause a spark in air is observed to be about at STP. What is the ratio of the magnitude of the field you calculated in the previous part to the observed value at STP? (f) What is it reasonable to conclude about this model of how air becomes ionized? (1) Since we used accurate numbers, this is a huge discrepancy, and the model is wrong. (2) Considering the approximations we made, this is pretty good agreement, and the model may be correct.
If the magnitude of the electric field in air exceeds roughly , the air break down and a spark forms. For a two-disk capacitor of radius 51 cm with a gap of 2 mm, if the electric field inside is just high enough that a spark occurs, what is the strength of the fringe field just outside the center of the capacitor?
94% of StudySmarter users get better grades.Sign up for free